# 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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### Deformation and rupture of compound cells under shear: A discrete multiphysics study

Physics of Fluids, Volume 31, Issue 5, May 2019.

This paper develops a three-dimensional numerical model for the simulation of cells in simple shear flow. The model is based on Discrete Multi-Physics (DMP), a meshless particle-based method that couples the smoothed particle hydrodynamics and the mass-spring model. In this study, the effect of the nucleus in cells is investigated for a broad range of capillary numbers. It is shown that the nucleus size affects the deformation of the cell. Moreover, oscillations are observed in the tank-treading motion of the membrane when capillary number and nucleus size are both sufficiently large. Additionally, DMP shows that the cell and nuclei may experience rupture under extreme flow conditions.

This paper develops a three-dimensional numerical model for the simulation of cells in simple shear flow. The model is based on Discrete Multi-Physics (DMP), a meshless particle-based method that couples the smoothed particle hydrodynamics and the mass-spring model. In this study, the effect of the nucleus in cells is investigated for a broad range of capillary numbers. It is shown that the nucleus size affects the deformation of the cell. Moreover, oscillations are observed in the tank-treading motion of the membrane when capillary number and nucleus size are both sufficiently large. Additionally, DMP shows that the cell and nuclei may experience rupture under extreme flow conditions.

Categories: Latest papers in fluid mechanics

### On the relevance of kinematics for cavitation implosion loads

Physics of Fluids, Volume 31, Issue 5, May 2019.

This study presents a novel physical model to convert the potential energy contained in vaporous cavitation into local surface impact power and an acoustic pressure signature caused by the violent collapse of these cavities in a liquid. The model builds on an analytical representation of the solid angle projection approach by Leclercq et al. [“Numerical cavitation intensity on a hydrofoil for 3D homogeneous unsteady viscous flows,” Int. J. Fluid Mach. Syst. 10, 254–263 (2017)]. It is applied as a runtime post-processing tool in numerical simulations of cavitating flows. In the present study, the model is inspected in light of the time accurate energy balance during the cavity collapse. Analytical considerations show that the potential cavity energy is first converted into kinetic energy in the surrounding liquid [D. Obreschkow et al., “Cavitation bubble dynamics inside liquid drops in microgravity,” Phys. Rev. Lett. 97, 094502 (2006)] and focused in space before the conversion into shock wave energy takes place. To this end, the physical model is complemented by an energy conservative transport function that can focus the potential cavity energy into the collapse center before it is converted into acoustic power. The formulation of the energy focusing equation is based on a Eulerian representation of the flow. The improved model is shown to provide physical results for the acoustic wall pressure obtained from the numerical simulation of a close-wall vapor bubble cloud collapse.

This study presents a novel physical model to convert the potential energy contained in vaporous cavitation into local surface impact power and an acoustic pressure signature caused by the violent collapse of these cavities in a liquid. The model builds on an analytical representation of the solid angle projection approach by Leclercq et al. [“Numerical cavitation intensity on a hydrofoil for 3D homogeneous unsteady viscous flows,” Int. J. Fluid Mach. Syst. 10, 254–263 (2017)]. It is applied as a runtime post-processing tool in numerical simulations of cavitating flows. In the present study, the model is inspected in light of the time accurate energy balance during the cavity collapse. Analytical considerations show that the potential cavity energy is first converted into kinetic energy in the surrounding liquid [D. Obreschkow et al., “Cavitation bubble dynamics inside liquid drops in microgravity,” Phys. Rev. Lett. 97, 094502 (2006)] and focused in space before the conversion into shock wave energy takes place. To this end, the physical model is complemented by an energy conservative transport function that can focus the potential cavity energy into the collapse center before it is converted into acoustic power. The formulation of the energy focusing equation is based on a Eulerian representation of the flow. The improved model is shown to provide physical results for the acoustic wall pressure obtained from the numerical simulation of a close-wall vapor bubble cloud collapse.

Categories: Latest papers in fluid mechanics

### Rotational instabilities in microchannel flows

Physics of Fluids, Volume 31, Issue 5, May 2019.

Mixing in numerous medical and chemical applications, involving overly long microchannels, can be enhanced by inducing flow instabilities. The channel length is thus shortened in the inertial microfluidics regime due to the enhanced mixing, thereby making the device compact and portable. Motivated by the emerging applications of a lab on a compact disk based microfluidic devices, we analyze the linear stability of rotationally actuated microchannel flows commonly deployed for biochemical and biomedical applications. The solution of the coupled system of Orr-Sommerfeld and Squire equations yields the growth rate and the neutral curves for the Coriolis force-driven instability. We report on the existence of four different types of unstable modes (Type-I to Type-IV) at low rotation numbers. Furthermore, Types-I and II exhibit competing characteristics, signifying that Type-II can play an important role in the transition to turbulence. Type-III and Type-IV modes have relatively lower growth rates, but the associated normal velocity has an oscillatory nature near the center of the channel. Thus, we infer that Types-III and IV might cause strong mixing locally by virtue of strong velocity perturbation in proximity to the various point depths. Moreover, the situation is reliable if the channel is too short to allow for the amplification of Types-I and II. We quantify the potential of all the unstable modes to induce such localized mixing near an imaginary interface (near a hyphothetical interface) inside the flow using the notion of penetration depth. This study also presents an instability regime diagram obtained from the parametric study over a range of Reynolds numbers, rotation numbers, and streamwise and spanwise wavenumbers to assist the design of efficient microchannels. Further insight into the mechanism of energy transfer, drawn from the evaluation of the kinetic-energy budget, reveals how the Reynolds stress first transfers energy from the mean flow to the streamwise velocity fluctuations. The Coriolis force, thereafter, redistributes the axial momentum into spanwise and wall-normal directions, generating the frequently observed roll-cell structures. A qualitative comparison of our predictions with the reported experiments on roll-cells indicates a good agreement.

Mixing in numerous medical and chemical applications, involving overly long microchannels, can be enhanced by inducing flow instabilities. The channel length is thus shortened in the inertial microfluidics regime due to the enhanced mixing, thereby making the device compact and portable. Motivated by the emerging applications of a lab on a compact disk based microfluidic devices, we analyze the linear stability of rotationally actuated microchannel flows commonly deployed for biochemical and biomedical applications. The solution of the coupled system of Orr-Sommerfeld and Squire equations yields the growth rate and the neutral curves for the Coriolis force-driven instability. We report on the existence of four different types of unstable modes (Type-I to Type-IV) at low rotation numbers. Furthermore, Types-I and II exhibit competing characteristics, signifying that Type-II can play an important role in the transition to turbulence. Type-III and Type-IV modes have relatively lower growth rates, but the associated normal velocity has an oscillatory nature near the center of the channel. Thus, we infer that Types-III and IV might cause strong mixing locally by virtue of strong velocity perturbation in proximity to the various point depths. Moreover, the situation is reliable if the channel is too short to allow for the amplification of Types-I and II. We quantify the potential of all the unstable modes to induce such localized mixing near an imaginary interface (near a hyphothetical interface) inside the flow using the notion of penetration depth. This study also presents an instability regime diagram obtained from the parametric study over a range of Reynolds numbers, rotation numbers, and streamwise and spanwise wavenumbers to assist the design of efficient microchannels. Further insight into the mechanism of energy transfer, drawn from the evaluation of the kinetic-energy budget, reveals how the Reynolds stress first transfers energy from the mean flow to the streamwise velocity fluctuations. The Coriolis force, thereafter, redistributes the axial momentum into spanwise and wall-normal directions, generating the frequently observed roll-cell structures. A qualitative comparison of our predictions with the reported experiments on roll-cells indicates a good agreement.

Categories: Latest papers in fluid mechanics

### Cavitation and ventilation modalities during ditching

Physics of Fluids, Volume 31, Issue 5, May 2019.

The flow taking place in the rear part of the fuselage during the emergency landing on water is investigated experimentally in realistic conditions. To this aim, tests on a double curvature specimen have been performed at horizontal velocities ranging from 21 m/s to 45 m/s. Test data highlight different cavitation and/or ventilation modalities which are strongly dependent on the horizontal velocity, with substantial changes in the flow features occurring with velocity variations of few meters per second. For the specimen considered here, the inception of the cavitation is found at about 30 m/s, confirming that scaled model tests performed at small horizontal velocities are unable to capture the hydrodynamics correctly. By analyzing pressure data, underwater movies, and force measurements, it is shown that the transition from the cavitation to ventilation condition has a significant effect on the longitudinal distribution of the loading which, together with inertia, aerodynamic loads, and engine thrust, governs the aircraft dynamics.

The flow taking place in the rear part of the fuselage during the emergency landing on water is investigated experimentally in realistic conditions. To this aim, tests on a double curvature specimen have been performed at horizontal velocities ranging from 21 m/s to 45 m/s. Test data highlight different cavitation and/or ventilation modalities which are strongly dependent on the horizontal velocity, with substantial changes in the flow features occurring with velocity variations of few meters per second. For the specimen considered here, the inception of the cavitation is found at about 30 m/s, confirming that scaled model tests performed at small horizontal velocities are unable to capture the hydrodynamics correctly. By analyzing pressure data, underwater movies, and force measurements, it is shown that the transition from the cavitation to ventilation condition has a significant effect on the longitudinal distribution of the loading which, together with inertia, aerodynamic loads, and engine thrust, governs the aircraft dynamics.

Categories: Latest papers in fluid mechanics

### Flow-induced vibration of a flexible triangular cable at low Reynolds numbers

Physics of Fluids, Volume 31, Issue 5, May 2019.

Flow-induced vibrations of an infinite long flexible cable with a triangular cross section allowed to oscillate in the cross-flow direction are numerically studied based on a high-order spectral element method at Re = 100 and 200. A tensioned beam model governs the dynamics of the triangular cable and the selected tension leads to single wave vibrations. The main focus of the present study is to explore the response of the flexible triangular cable, with the aim of providing new insights into the essential features of flow-induced vibrations of the long flexible body with an asymmetric cross section. The numerical results show that for the angle of attack α = 60° in which one of the sides of the triangular cable is facing the incoming flow, the oscillation of the cable is dominated by vortex-induced vibrations (VIVs) at Re = 100, while a combination of strong VIV and weak galloping is excited at Re = 200. As compared to the flow past a flexible cable with a circular cross section at the same conditions, the dynamics responses of the triangular cable are significantly vigorous, which is evidenced further in energy transfers and wake dynamics as well. It is also revealed that the secondary vortex generated at the trailing edge of the triangle plays an important role in the wake evolution process. Finally, additional simulations at α = 0° are conducted and the results show that the responses are suppressed strikingly with very weak amplitudes, implying that the wake dynamics is desynchronized against the vibration of the flexible cable.

Flow-induced vibrations of an infinite long flexible cable with a triangular cross section allowed to oscillate in the cross-flow direction are numerically studied based on a high-order spectral element method at Re = 100 and 200. A tensioned beam model governs the dynamics of the triangular cable and the selected tension leads to single wave vibrations. The main focus of the present study is to explore the response of the flexible triangular cable, with the aim of providing new insights into the essential features of flow-induced vibrations of the long flexible body with an asymmetric cross section. The numerical results show that for the angle of attack α = 60° in which one of the sides of the triangular cable is facing the incoming flow, the oscillation of the cable is dominated by vortex-induced vibrations (VIVs) at Re = 100, while a combination of strong VIV and weak galloping is excited at Re = 200. As compared to the flow past a flexible cable with a circular cross section at the same conditions, the dynamics responses of the triangular cable are significantly vigorous, which is evidenced further in energy transfers and wake dynamics as well. It is also revealed that the secondary vortex generated at the trailing edge of the triangle plays an important role in the wake evolution process. Finally, additional simulations at α = 0° are conducted and the results show that the responses are suppressed strikingly with very weak amplitudes, implying that the wake dynamics is desynchronized against the vibration of the flexible cable.

Categories: Latest papers in fluid mechanics

### Geometric optimization of riblet-textured surfaces for drag reduction in laminar boundary layer flows

Physics of Fluids, Volume 31, Issue 5, May 2019.

Micro-scale riblets are shown to systematically modify viscous skin friction in laminar flows at high Reynolds numbers. The textured denticles of native sharkskin are widely cited as a natural example of this passive drag reduction mechanism. Since the structure of a viscous boundary layer evolves along the plate, the local frictional drag changes are known empirically to be a function of the length of the plate in the flow direction, as well as the riblet spacing, and the ratio of the height to spacing of the riblets. Here, we aim to establish a canonical theory for high Reynolds number laminar flow over V-groove riblets to explore the self-similarity of the velocity profiles and the evolution of the total frictional drag exerted on plates of different lengths. Scaling analysis, conformal mapping, and numerical calculations are combined to show that the potential drag reduction achieved using riblet surfaces depends on an appropriately rescaled form of the Reynolds number and on the aspect ratio of the riblets (defined in terms of the ratio of the height to spacing of the texture). We show that riblet surfaces require a scaled Reynolds number lower than a maximum threshold to be drag-reducing and that the change in drag is a nonmonotonic function of the aspect ratio of the riblet texture. This physical scaling and the computational results presented here can be used to explain the underlying physical mechanism of this mode of passive drag reduction to rationalize the geometric dimensions of shark denticles, as well as the results of experiments with shark denticle replicas of various sizes, and guide designs for optimizing the textural parameters that result in friction-reducing surfaces.

Micro-scale riblets are shown to systematically modify viscous skin friction in laminar flows at high Reynolds numbers. The textured denticles of native sharkskin are widely cited as a natural example of this passive drag reduction mechanism. Since the structure of a viscous boundary layer evolves along the plate, the local frictional drag changes are known empirically to be a function of the length of the plate in the flow direction, as well as the riblet spacing, and the ratio of the height to spacing of the riblets. Here, we aim to establish a canonical theory for high Reynolds number laminar flow over V-groove riblets to explore the self-similarity of the velocity profiles and the evolution of the total frictional drag exerted on plates of different lengths. Scaling analysis, conformal mapping, and numerical calculations are combined to show that the potential drag reduction achieved using riblet surfaces depends on an appropriately rescaled form of the Reynolds number and on the aspect ratio of the riblets (defined in terms of the ratio of the height to spacing of the texture). We show that riblet surfaces require a scaled Reynolds number lower than a maximum threshold to be drag-reducing and that the change in drag is a nonmonotonic function of the aspect ratio of the riblet texture. This physical scaling and the computational results presented here can be used to explain the underlying physical mechanism of this mode of passive drag reduction to rationalize the geometric dimensions of shark denticles, as well as the results of experiments with shark denticle replicas of various sizes, and guide designs for optimizing the textural parameters that result in friction-reducing surfaces.

Categories: Latest papers in fluid mechanics

### A direct numerical simulation study of the influence of flame-generated vorticity on reaction-zone-surface area in weakly turbulent premixed combustion

Physics of Fluids, Volume 31, Issue 5, May 2019.

Direct numerical simulation data obtained from two statistically stationary, one-dimensional, planar, weakly turbulent, premixed flames are analyzed in order to examine the influence of flame-generated vorticity on the surface area of the reaction zone. The two flames are associated with the flamelet combustion regime and are characterized by two significantly different density ratios σ = 7.53 and 2.5, with all other things being roughly equal. The obtained results indicate that generation of vorticity due to baroclinic torque within flamelets can impede wrinkling of the reaction surface, reduce its area, and, hence, decrease the burning rate. Thus, these results call for revisiting the widely accepted concept of combustion acceleration due to flame-generated turbulence. In particular, in the case of σ = 7.53, the local stretch rate, which quantifies the local rate of increase or decrease in the surface area, is predominantly negative in regions characterized by a large magnitude of enstrophy or a large magnitude of the baroclinic torque term in the enstrophy transport equation, with the effect being more pronounced at larger values of the mean combustion progress variable. If the density ratio is low, e.g., σ = 2.5, the baroclinic torque weakly affects the vorticity field within the mean flame brush and the aforementioned effect is not pronounced.

Direct numerical simulation data obtained from two statistically stationary, one-dimensional, planar, weakly turbulent, premixed flames are analyzed in order to examine the influence of flame-generated vorticity on the surface area of the reaction zone. The two flames are associated with the flamelet combustion regime and are characterized by two significantly different density ratios σ = 7.53 and 2.5, with all other things being roughly equal. The obtained results indicate that generation of vorticity due to baroclinic torque within flamelets can impede wrinkling of the reaction surface, reduce its area, and, hence, decrease the burning rate. Thus, these results call for revisiting the widely accepted concept of combustion acceleration due to flame-generated turbulence. In particular, in the case of σ = 7.53, the local stretch rate, which quantifies the local rate of increase or decrease in the surface area, is predominantly negative in regions characterized by a large magnitude of enstrophy or a large magnitude of the baroclinic torque term in the enstrophy transport equation, with the effect being more pronounced at larger values of the mean combustion progress variable. If the density ratio is low, e.g., σ = 2.5, the baroclinic torque weakly affects the vorticity field within the mean flame brush and the aforementioned effect is not pronounced.

Categories: Latest papers in fluid mechanics

### Pumping flow model in a microchannel with propagative rhythmic membrane contraction

Physics of Fluids, Volume 31, Issue 5, May 2019.

A pumping flow model in a microchannel with a single attached membrane subjected to propagative contraction is presented in this article. The lubrication theory is used to approximate the induced flow field at a low Reynolds number flow regime. A well-posed expression for the wall profile is derived to describe the membrane propagative mode of rhythmic contractions. Unlike our previously derived pumping model “nonpropagative” where at least two membranes that operate with time-lag are required to produce unidirectional flow, the present results demonstrate that an inelastic channel with a single membrane contraction that operates in a “propagative” mode can produce unidirectional flow and work as a micropump. The model can be used to understand flow transport in many biological systems including but not limited to insect respiration, urine flow, and fluid dynamics of duodenum and intestine. The present pumping paradigm is relatively easy to fabricate and is expected to be useful in many biomedical applications.

A pumping flow model in a microchannel with a single attached membrane subjected to propagative contraction is presented in this article. The lubrication theory is used to approximate the induced flow field at a low Reynolds number flow regime. A well-posed expression for the wall profile is derived to describe the membrane propagative mode of rhythmic contractions. Unlike our previously derived pumping model “nonpropagative” where at least two membranes that operate with time-lag are required to produce unidirectional flow, the present results demonstrate that an inelastic channel with a single membrane contraction that operates in a “propagative” mode can produce unidirectional flow and work as a micropump. The model can be used to understand flow transport in many biological systems including but not limited to insect respiration, urine flow, and fluid dynamics of duodenum and intestine. The present pumping paradigm is relatively easy to fabricate and is expected to be useful in many biomedical applications.

Categories: Latest papers in fluid mechanics

### Response modes of erythrocytes in high-frequency oscillatory shear flows

Physics of Fluids, Volume 31, Issue 5, May 2019.

Due to its capability of duplicating the deformation scenario of erythrocytes (red blood cells), in in vivo time scales, passing through interendothelial slits in the spleen, the understanding of the dynamic response of erythrocytes in oscillatory shear flows is of critical importance to the development of an effective in vitro methodology to study the mechanics, metabolism, and aging procedure in vivo [R. Asaro et al., “Erythrocyte aging, protection via vesiculation: An analysis methodology via oscillatory flow,” Front. Physiol. 9, 1607 (2018)]. Accordingly, we conducted a systematic computational investigation of the dynamics of erythrocytes in high-frequency oscillatory shear flows by using a fluid-cell interaction model based on the Stokes-flow framework and a multiscale structural depiction of the cell. Within the range of parameters we consider, we identify five different response modes (wheeling, tilted wheeling, tank treading mode 1, tank treading mode 2, and irregular). The occurrence and stability of these response modes depend on the frequency of the flow, the peak capillary number, the viscosity ratio, the initial orientation of the cell, and the stress-free state of the protein skeleton. Through long-term simulations [[math] periods], mode switching events have been discovered, during which the cell transfers from one mode to another, often via an intermediate transient mode. The deformation of the skeleton and the contact stress between the skeleton and the lipid bilayer are computed since these are of direct importance to describing vital cell phenomena such as vesiculation by which the cell protects itself from premature elimination.

Due to its capability of duplicating the deformation scenario of erythrocytes (red blood cells), in in vivo time scales, passing through interendothelial slits in the spleen, the understanding of the dynamic response of erythrocytes in oscillatory shear flows is of critical importance to the development of an effective in vitro methodology to study the mechanics, metabolism, and aging procedure in vivo [R. Asaro et al., “Erythrocyte aging, protection via vesiculation: An analysis methodology via oscillatory flow,” Front. Physiol. 9, 1607 (2018)]. Accordingly, we conducted a systematic computational investigation of the dynamics of erythrocytes in high-frequency oscillatory shear flows by using a fluid-cell interaction model based on the Stokes-flow framework and a multiscale structural depiction of the cell. Within the range of parameters we consider, we identify five different response modes (wheeling, tilted wheeling, tank treading mode 1, tank treading mode 2, and irregular). The occurrence and stability of these response modes depend on the frequency of the flow, the peak capillary number, the viscosity ratio, the initial orientation of the cell, and the stress-free state of the protein skeleton. Through long-term simulations [[math] periods], mode switching events have been discovered, during which the cell transfers from one mode to another, often via an intermediate transient mode. The deformation of the skeleton and the contact stress between the skeleton and the lipid bilayer are computed since these are of direct importance to describing vital cell phenomena such as vesiculation by which the cell protects itself from premature elimination.

Categories: Latest papers in fluid mechanics

### Natural convection flow of a hybrid nanofluid in a square enclosure partially filled with a porous medium using a thermal non-equilibrium model

Physics of Fluids, Volume 31, Issue 4, April 2019.

Buoyancy-driven flow inside a superposed enclosure filled with composite porous-hybrid nanofluid layers was investigated numerically using a local thermal nonequilibrium model for the heat transfer between the fluid and the solid phases. The bottom wall of the enclosure was partly heated to provide a heat flux, while the other parts of the wall were thermally insulated. The top and vertical walls of the enclosure were maintained at constant cold temperatures. The Darcy-Brinkman model was adopted to model the flow inside the porous layer. The Galerkin finite element method was used to solve the governing equations using the semi-implicit method for pressure linked equations algorithm. The selected parameters are presented for the Rayleigh number (Ra), 103 ≤ Ra ≤ 107, the Darcy number (Da), 10−7 ≤ Da ≤ 1, the porous layer thickness (S), 0 ≤ S ≤ 1, the modified conductivity ratio (γ), 10−1 ≤ γ ≤ 104, the interphase heat transfer coefficient (H), 10−1 ≤ H ≤ 1000, the heat source length (B), 0.2, 0.4, 0.6, 0.8 and 1, and the nanoparticle volume fraction (ϕ), 0 ≤ ϕ ≤ 0.2. It has been concluded that the rate of heat transfer of hybrid nanofluid (Cu−Al2O3/water) is higher than with the pure fluid. Furthermore, at Ra ≤ 105, the heat transfer rate maintains its maximum value when S reaches the critical value (S = 0.3). The values of S, Da, and B were found to have a significant effect on the heat removal from the heat source. Increasing the values of γ and H can strongly enhance the heat transfer rate and satisfy the thermal equilibrium case.

Buoyancy-driven flow inside a superposed enclosure filled with composite porous-hybrid nanofluid layers was investigated numerically using a local thermal nonequilibrium model for the heat transfer between the fluid and the solid phases. The bottom wall of the enclosure was partly heated to provide a heat flux, while the other parts of the wall were thermally insulated. The top and vertical walls of the enclosure were maintained at constant cold temperatures. The Darcy-Brinkman model was adopted to model the flow inside the porous layer. The Galerkin finite element method was used to solve the governing equations using the semi-implicit method for pressure linked equations algorithm. The selected parameters are presented for the Rayleigh number (Ra), 103 ≤ Ra ≤ 107, the Darcy number (Da), 10−7 ≤ Da ≤ 1, the porous layer thickness (S), 0 ≤ S ≤ 1, the modified conductivity ratio (γ), 10−1 ≤ γ ≤ 104, the interphase heat transfer coefficient (H), 10−1 ≤ H ≤ 1000, the heat source length (B), 0.2, 0.4, 0.6, 0.8 and 1, and the nanoparticle volume fraction (ϕ), 0 ≤ ϕ ≤ 0.2. It has been concluded that the rate of heat transfer of hybrid nanofluid (Cu−Al2O3/water) is higher than with the pure fluid. Furthermore, at Ra ≤ 105, the heat transfer rate maintains its maximum value when S reaches the critical value (S = 0.3). The values of S, Da, and B were found to have a significant effect on the heat removal from the heat source. Increasing the values of γ and H can strongly enhance the heat transfer rate and satisfy the thermal equilibrium case.

Categories: Latest papers in fluid mechanics

### Water column impact on a rigid wall with air cavity effects

Physics of Fluids, Volume 31, Issue 4, April 2019.

Water column impacts on a rigid wall without and with air cavity entrapment are investigated based on potential-flow theory without considering the gravity effect. A boundary element method is employed to simulate the entire hydrodynamic process, with an introduced decoupling technique of a shallow-water approximation to tackle the thin jet difficulty in impact problems. Numerical techniques to deal with processes including the cavity jet impingement and fluid immersion are also introduced. Numerical simulations are carried out for water column impact processes with cavities of different volumes, shapes, and initial pressures inside. Theoretical deductions are performed for the limiting case of impact without air cavity at the initial and steady state. From the energy point of view, an energy transfer relation is established to achieve a quantitative prediction of the maximum pressure in a deforming cavity in a general impact process. Quantitative analysis is made to assess the effects of the initial nondimensional potential energy of the cavity on the maximum cavity pressure during the impact. Interesting phenomena such as the inner jet generated away from the impact surface are observed and discussed.

Water column impacts on a rigid wall without and with air cavity entrapment are investigated based on potential-flow theory without considering the gravity effect. A boundary element method is employed to simulate the entire hydrodynamic process, with an introduced decoupling technique of a shallow-water approximation to tackle the thin jet difficulty in impact problems. Numerical techniques to deal with processes including the cavity jet impingement and fluid immersion are also introduced. Numerical simulations are carried out for water column impact processes with cavities of different volumes, shapes, and initial pressures inside. Theoretical deductions are performed for the limiting case of impact without air cavity at the initial and steady state. From the energy point of view, an energy transfer relation is established to achieve a quantitative prediction of the maximum pressure in a deforming cavity in a general impact process. Quantitative analysis is made to assess the effects of the initial nondimensional potential energy of the cavity on the maximum cavity pressure during the impact. Interesting phenomena such as the inner jet generated away from the impact surface are observed and discussed.

Categories: Latest papers in fluid mechanics

### Insights into the physics of dominating frequency modes for flow past a stationary sphere: Direct numerical simulations

Physics of Fluids, Volume 31, Issue 4, April 2019.

Direct numerical simulations are carried out for an incompressible flow past a stationary sphere, in the range of 100 ≤ Re ≤ 1000. It is found that the first instability occurs as the axisymmetric wake undergoes breakage at Re ≥ 250. Adding small perturbations to the flow showed that the preferred direction of breakage of the axisymmetric wake and the corresponding contribution of the y and z-direction lift coefficients are highly sensitive and get randomly affected even due to slightest perturbations that might get induced. The second instability arises at Re = 300 as large-scale hairpin shaped structures are formed and shed periodically at frequency StVS = 0.134. At Re = 350, the highly regular hairpin shedding pattern undergoes a quasiperiodic change. From the Q-criterion isosurface, we observed that the quasiperiodicity is induced due to the formation and shedding of secondary hairpin structures which are alongside the primary ones. These secondary hairpin structures are of discernable orientations and are shed 4 times slower as compared to the primary hairpins at Re = 350. Identification of these secondary hairpin structures confirms the hypothesis of wake modulation. The low-frequency mode (Stm) is captured when energy spectral analysis is performed on the surface integrated instantaneous force coefficients and on the radial velocities. The low-frequency mode further exists at all higher Re, exhibiting a gradual increase in Stm. At Re ≥ 800, shear layer instabilities are manifested, demonstrating a characteristic peak at StKH = 0.32 in the energy spectra, rendering the mean lift coefficients to become zero again.

Direct numerical simulations are carried out for an incompressible flow past a stationary sphere, in the range of 100 ≤ Re ≤ 1000. It is found that the first instability occurs as the axisymmetric wake undergoes breakage at Re ≥ 250. Adding small perturbations to the flow showed that the preferred direction of breakage of the axisymmetric wake and the corresponding contribution of the y and z-direction lift coefficients are highly sensitive and get randomly affected even due to slightest perturbations that might get induced. The second instability arises at Re = 300 as large-scale hairpin shaped structures are formed and shed periodically at frequency StVS = 0.134. At Re = 350, the highly regular hairpin shedding pattern undergoes a quasiperiodic change. From the Q-criterion isosurface, we observed that the quasiperiodicity is induced due to the formation and shedding of secondary hairpin structures which are alongside the primary ones. These secondary hairpin structures are of discernable orientations and are shed 4 times slower as compared to the primary hairpins at Re = 350. Identification of these secondary hairpin structures confirms the hypothesis of wake modulation. The low-frequency mode (Stm) is captured when energy spectral analysis is performed on the surface integrated instantaneous force coefficients and on the radial velocities. The low-frequency mode further exists at all higher Re, exhibiting a gradual increase in Stm. At Re ≥ 800, shear layer instabilities are manifested, demonstrating a characteristic peak at StKH = 0.32 in the energy spectra, rendering the mean lift coefficients to become zero again.

Categories: Latest papers in fluid mechanics

### Large-eddy simulation of Sandia Flame F using structural subgrid-scale models and partially-stirred-reactor approach

Physics of Fluids, Volume 31, Issue 4, April 2019.

Owing to the strong interaction between turbulence and combustion, it is particularly challenging to accurately predict local flame extinctions in a turbulent flame at high Reynolds numbers. Subgrid-scale (SGS) parameterization and model for calculating the filtered reaction rates are the main determinants of an accurate large-eddy simulation (LES) of turbulent flow. This study integrates the recently introduced gradient-type structural SGS models with a simplified partially-stirred-reactor approach to simulate a piloted partially premixed jet flame, Sandia Flame F. An advantage of using the nonlinear SGS models is that they can provide reverse energy transfer from subgrid to resolved scales. To quantitatively understand the performance of the LES framework, we have comprehensively compared temperature and mass fractions of major and minor species with experimental data. The statistics of the simulated field show good agreement with measurements and a notable improvement over previous simulations. Results support the assertion that the proposed nonlinear LES framework can capture extinction and re-ignition in turbulent flames with reasonable computational cost.

Owing to the strong interaction between turbulence and combustion, it is particularly challenging to accurately predict local flame extinctions in a turbulent flame at high Reynolds numbers. Subgrid-scale (SGS) parameterization and model for calculating the filtered reaction rates are the main determinants of an accurate large-eddy simulation (LES) of turbulent flow. This study integrates the recently introduced gradient-type structural SGS models with a simplified partially-stirred-reactor approach to simulate a piloted partially premixed jet flame, Sandia Flame F. An advantage of using the nonlinear SGS models is that they can provide reverse energy transfer from subgrid to resolved scales. To quantitatively understand the performance of the LES framework, we have comprehensively compared temperature and mass fractions of major and minor species with experimental data. The statistics of the simulated field show good agreement with measurements and a notable improvement over previous simulations. Results support the assertion that the proposed nonlinear LES framework can capture extinction and re-ignition in turbulent flames with reasonable computational cost.

Categories: Latest papers in fluid mechanics

### Instantaneous linear stability of plane Poiseuille flow forced by spanwise oscillations

Physics of Fluids, Volume 31, Issue 4, April 2019.

In the present work, the stability of a plane Poiseuille flow forced by spanwise oscillations is studied via the instantaneous linear stability theory (LST). For streamwise Poiseuille flow and a spanwise Stokes layer, the superposition of these two linearly stable flows can lead to transient growth of perturbations. Periodic and aperiodic growth rates over time are found. Mode-crossing is observed in the aperiodic mode. Effects of oscillation amplitude W0 and frequency Ω are studied. The maximum instantaneous growth rate increases with increasing W0. At low W0, the stability of the flow is dominated by the corresponding Poiseuille flow or by the interactions between the two flows. At high W0, the stability characteristics of the Poiseuille–Stokes flow are very similar to those of the corresponding Stokes layer. It is demonstrated that oscillations have destabilizing effects in short-time intervals of one oscillation period. Oscillations of extremely low or high Ω have much weaker effects than those of medium Ω. The transient growth of the most unstable mode is traced by using direct numerical simulation (DNS). Instantaneous LST can capture the transient growth but fails to predict the accurate growth rate when the amplification ratio is higher than e9. The difference between LST and DNS is mainly due to the incorrect production of LST without nonlinear transportation. From the growing phase to the decay phase of the transient mode, the production term shifts from the destabilizing role to the stabilizing role because of the correlation-phase reversal of the perturbation velocities.

In the present work, the stability of a plane Poiseuille flow forced by spanwise oscillations is studied via the instantaneous linear stability theory (LST). For streamwise Poiseuille flow and a spanwise Stokes layer, the superposition of these two linearly stable flows can lead to transient growth of perturbations. Periodic and aperiodic growth rates over time are found. Mode-crossing is observed in the aperiodic mode. Effects of oscillation amplitude W0 and frequency Ω are studied. The maximum instantaneous growth rate increases with increasing W0. At low W0, the stability of the flow is dominated by the corresponding Poiseuille flow or by the interactions between the two flows. At high W0, the stability characteristics of the Poiseuille–Stokes flow are very similar to those of the corresponding Stokes layer. It is demonstrated that oscillations have destabilizing effects in short-time intervals of one oscillation period. Oscillations of extremely low or high Ω have much weaker effects than those of medium Ω. The transient growth of the most unstable mode is traced by using direct numerical simulation (DNS). Instantaneous LST can capture the transient growth but fails to predict the accurate growth rate when the amplification ratio is higher than e9. The difference between LST and DNS is mainly due to the incorrect production of LST without nonlinear transportation. From the growing phase to the decay phase of the transient mode, the production term shifts from the destabilizing role to the stabilizing role because of the correlation-phase reversal of the perturbation velocities.

Categories: Latest papers in fluid mechanics

### Interfacial instabilities of immiscible non-Newtonian radial displacements in porous media

Physics of Fluids, Volume 31, Issue 4, April 2019.

Immiscible flows that involve radial displacements of shear-thinning or shear-thickening fluids by a Newtonian fluid in a homogeneous porous medium are modeled numerically. The interfacial instabilities are tracked in time for different values of the rheological parameters, namely, the Deborah number (De) and the power-law index (n), and are characterized through the effective number of fingers and the finger area density. The results of the study reveal that the effects of these two parameters on the instability are not monotonic, and it is found that the flow is least unstable for some critical value of either De or n. The dependence of these critical values, in particular, on the mobility ratio (M) and capillary number (Ca) is analyzed. It is found that when all other parameters are fixed, the critical Deborah number (Dec) increases as the power-law index increases in shear-thinning fluids or decreases in shear-thickening ones. Similarly, the critical power-law index (nc) increases with increasing (decreasing) Deborah number in shear-thinning (shear-thickening) flows. Furthermore, both critical parameters are found to vary monotonically with the mobility ratio, with the dependence most noticeable at small values of M. Their variation with the capillary number is however nonmonotonic reaching an extremum at an intermediate value of Ca. An examination of the rate of shear strain at the interface reveals that it consistently shows the smoothest variation and the smallest average value at the critical parameter.

Immiscible flows that involve radial displacements of shear-thinning or shear-thickening fluids by a Newtonian fluid in a homogeneous porous medium are modeled numerically. The interfacial instabilities are tracked in time for different values of the rheological parameters, namely, the Deborah number (De) and the power-law index (n), and are characterized through the effective number of fingers and the finger area density. The results of the study reveal that the effects of these two parameters on the instability are not monotonic, and it is found that the flow is least unstable for some critical value of either De or n. The dependence of these critical values, in particular, on the mobility ratio (M) and capillary number (Ca) is analyzed. It is found that when all other parameters are fixed, the critical Deborah number (Dec) increases as the power-law index increases in shear-thinning fluids or decreases in shear-thickening ones. Similarly, the critical power-law index (nc) increases with increasing (decreasing) Deborah number in shear-thinning (shear-thickening) flows. Furthermore, both critical parameters are found to vary monotonically with the mobility ratio, with the dependence most noticeable at small values of M. Their variation with the capillary number is however nonmonotonic reaching an extremum at an intermediate value of Ca. An examination of the rate of shear strain at the interface reveals that it consistently shows the smoothest variation and the smallest average value at the critical parameter.

Categories: Latest papers in fluid mechanics

### Instability of two-dimensional square eddy flows

Physics of Fluids, Volume 31, Issue 4, April 2019.

Plane nonparallel flow in a square fluid domain satisfying free-slip boundary condition is examined. The energy dissipation of the flow is controlled by viscosity and linear friction, which is from the friction effect of Hartmann bottom boundary layer in three-dimensional magnetohydrodynamic experiment in a cell bottomed with the square domain. For the four eddy basic flow of the problem, there exist two bicritical parameters corresponding to the existence of two neutral eigenfunction spaces, respectively. The first neutral eigenfunction is one-dimensional and gives rise to the bifurcation of the basic flows into a pair of secondary flow, while the second one is two-dimensional and leads to the occurrence of a circle of secondary flows. These results are obtained numerically and can be approximated by elementary functions in a simple form. The secondary flows with respect to the first bicritical parameter exhibits the merging of diagonal eddies observed by Sommeria’s experiments on an inverse energy cascade to turbulence. More instability phenomena are displayed from the secondary flows with respect to the second bicritical parameter.

Plane nonparallel flow in a square fluid domain satisfying free-slip boundary condition is examined. The energy dissipation of the flow is controlled by viscosity and linear friction, which is from the friction effect of Hartmann bottom boundary layer in three-dimensional magnetohydrodynamic experiment in a cell bottomed with the square domain. For the four eddy basic flow of the problem, there exist two bicritical parameters corresponding to the existence of two neutral eigenfunction spaces, respectively. The first neutral eigenfunction is one-dimensional and gives rise to the bifurcation of the basic flows into a pair of secondary flow, while the second one is two-dimensional and leads to the occurrence of a circle of secondary flows. These results are obtained numerically and can be approximated by elementary functions in a simple form. The secondary flows with respect to the first bicritical parameter exhibits the merging of diagonal eddies observed by Sommeria’s experiments on an inverse energy cascade to turbulence. More instability phenomena are displayed from the secondary flows with respect to the second bicritical parameter.

Categories: Latest papers in fluid mechanics

### Proper orthogonal decomposition of primary breakup and spray in co-axial airblast atomizers

Physics of Fluids, Volume 31, Issue 4, April 2019.

The primary atomization of a liquid jet by a coaxial stream of high speed gas is analyzed by means of Proper Orthogonal Decomposition (POD) for gas to liquid momentum ratios (MR) from 182 to 727 and Weber numbers, We, from 22 to 88. The continuous liquid core is visualized by the optical connectivity technique. The full spray in the near nozzle region is visualized using shadowgraphy. It is found that universal POD modes exist for the continuous liquid core and the near nozzle full spray across all considered flow conditions. The universal POD modes are related to physical structures of the flow. The complexity of the flow, as determined by the energy of the POD modes, is found to be constant for the liquid core across the examined range of flow MR. On the contrary, the complexity of the full spray is inversely proportional to the flow MR. Correlations are established between the spatial and temporal scales of primary atomization. In addition, a novel method to extrapolate the spatial and temporal scales of the atomization process beyond the limits of the current measurement resolution is described and demonstrated. Estimates are provided on the number of samples and the sampling rate that are required to fully resolve the flow to specific temporal and spatial scales.

The primary atomization of a liquid jet by a coaxial stream of high speed gas is analyzed by means of Proper Orthogonal Decomposition (POD) for gas to liquid momentum ratios (MR) from 182 to 727 and Weber numbers, We, from 22 to 88. The continuous liquid core is visualized by the optical connectivity technique. The full spray in the near nozzle region is visualized using shadowgraphy. It is found that universal POD modes exist for the continuous liquid core and the near nozzle full spray across all considered flow conditions. The universal POD modes are related to physical structures of the flow. The complexity of the flow, as determined by the energy of the POD modes, is found to be constant for the liquid core across the examined range of flow MR. On the contrary, the complexity of the full spray is inversely proportional to the flow MR. Correlations are established between the spatial and temporal scales of primary atomization. In addition, a novel method to extrapolate the spatial and temporal scales of the atomization process beyond the limits of the current measurement resolution is described and demonstrated. Estimates are provided on the number of samples and the sampling rate that are required to fully resolve the flow to specific temporal and spatial scales.

Categories: Latest papers in fluid mechanics

### The formation mechanism of recirculating wake for steady flow through and around arrays of cylinders

Physics of Fluids, Volume 31, Issue 4, April 2019.

The mechanism of recirculating wake formation was examined based on a series of numerical experiments on steady flow through and around periodic square arrays of evenly spaced circular cylinders. The Reynolds number of the array Re ranged from 1 to 50, and the solid fraction of the array ϕ was varied from 9.69 × 10−11 to 0.785. The recirculating wake was found to be completely detached from the array under a certain range of ϕ and Re, and varied in size with ϕ and Re. The trailing edge bleeding from the array affects the vortex formation in a way consistent with the entrainment-detrainment mechanism. The combination effect of vorticity accumulation and decay also gives rise to the dissipative vortex. By examining the shear layer formed by the bleeding flow and outer flow, which varies with Re and ϕ, it is concluded that the recirculation mainly results from flow separation at the junction point between the shear layer and the extended centerline of the array due to an adverse pressure gradient.

The mechanism of recirculating wake formation was examined based on a series of numerical experiments on steady flow through and around periodic square arrays of evenly spaced circular cylinders. The Reynolds number of the array Re ranged from 1 to 50, and the solid fraction of the array ϕ was varied from 9.69 × 10−11 to 0.785. The recirculating wake was found to be completely detached from the array under a certain range of ϕ and Re, and varied in size with ϕ and Re. The trailing edge bleeding from the array affects the vortex formation in a way consistent with the entrainment-detrainment mechanism. The combination effect of vorticity accumulation and decay also gives rise to the dissipative vortex. By examining the shear layer formed by the bleeding flow and outer flow, which varies with Re and ϕ, it is concluded that the recirculation mainly results from flow separation at the junction point between the shear layer and the extended centerline of the array due to an adverse pressure gradient.

Categories: Latest papers in fluid mechanics

### Study of a nanodroplet breakup through many-body dissipative particle dynamics

Physics of Fluids, Volume 31, Issue 4, April 2019.

Breakup of a nanodroplet is a common phenomenon of great importance in the nanoprinting and the electrohydrodynamic jet printing, which affects the accuracy and efficiency of droplet delivery. When the diameter of a decaying jet reduces to nanometers, the breakup mechanism remains unclear because the traditional continuum theory fails. In this work, a mesoscale method, many-body dissipative particle dynamics, has been developed to investigate the breakup process of water, glycerol, and ethanol nanodroplets. Generally, a falling nanodroplet deforms and breaks up with the following stages, symmetrical deformation, thin-neck appearance, and drop-tip motion. The breakup time, the neck length, the minimum diameter of the neck before breakup, and the tip velocity of the formed tail after breakup have been examined. It is found that the neck length shows an exponential relationship with the time. Compared to the similarity solution near the separation point, the exponent relation between the minimum diameter of the neck and the reduced time has been verified. Moreover, the exponent (n) for different fluids can be roughly estimated by the Ohnesorge (Oh) number as n = 0.1015 log(Oh) + 0.6776. The tip velocity varies as the inverse square root of the reduced time when the tip shrinks slowly. When the tip shrinks rapidly, the exponential relationship between the tip velocity and the reduced time is predicted, which is also valid for shrinking a satellite droplet. This study provides a fundamental understanding of the nanodroplet breakup for improvement of their dynamical behaviors in a real application.

Breakup of a nanodroplet is a common phenomenon of great importance in the nanoprinting and the electrohydrodynamic jet printing, which affects the accuracy and efficiency of droplet delivery. When the diameter of a decaying jet reduces to nanometers, the breakup mechanism remains unclear because the traditional continuum theory fails. In this work, a mesoscale method, many-body dissipative particle dynamics, has been developed to investigate the breakup process of water, glycerol, and ethanol nanodroplets. Generally, a falling nanodroplet deforms and breaks up with the following stages, symmetrical deformation, thin-neck appearance, and drop-tip motion. The breakup time, the neck length, the minimum diameter of the neck before breakup, and the tip velocity of the formed tail after breakup have been examined. It is found that the neck length shows an exponential relationship with the time. Compared to the similarity solution near the separation point, the exponent relation between the minimum diameter of the neck and the reduced time has been verified. Moreover, the exponent (n) for different fluids can be roughly estimated by the Ohnesorge (Oh) number as n = 0.1015 log(Oh) + 0.6776. The tip velocity varies as the inverse square root of the reduced time when the tip shrinks slowly. When the tip shrinks rapidly, the exponential relationship between the tip velocity and the reduced time is predicted, which is also valid for shrinking a satellite droplet. This study provides a fundamental understanding of the nanodroplet breakup for improvement of their dynamical behaviors in a real application.

Categories: Latest papers in fluid mechanics

### Self-driven droplet transport: Effect of wettability gradient and confinement

Physics of Fluids, Volume 31, Issue 4, April 2019.

Surface tension driven droplet transport in an open surface is increasingly becoming popular for various microfluidic applications. In this work, efficient transport of a glycerin droplet on an open wettability gradient surface with controlled wettability and confinement is numerically investigated. Nondimensional track width [math]* (ratio of the width of the wettability gradient track [math] and the initial droplet diameter d0) of a wettability gradient track laid on a superhydrophobic background represents wettability confinement. A lower value of [math]* represents higher wettability confinement. Droplet behavior changes for different wettability confinements and gradients of the track. It is found that droplet velocity is a function of the wettability confinement and the gradient; droplet transport velocity is maximum for [math]* = 0.8. Higher confinement ([math]* < 0.8) leads to a significant reduction in droplet velocity. Droplet transport characteristics on hydrophilic–superhydrophilic, hydrophobic–superhydrophilic, and superhydrophobic–superhydrophilic tracks are studied. It is found that for a fixed length of the track, droplet velocity is maximum for the superhydrophobic–superhydrophilic track. A droplet transport regime is demonstrated for a wettability gradient track with different confinements, and it is found that the droplet is transported for wettability confinement [math]* > 0.6 irrespective of the wettability gradient of the track. These findings provide valuable insight into efficient droplet manipulation in microfluidic devices.

Surface tension driven droplet transport in an open surface is increasingly becoming popular for various microfluidic applications. In this work, efficient transport of a glycerin droplet on an open wettability gradient surface with controlled wettability and confinement is numerically investigated. Nondimensional track width [math]* (ratio of the width of the wettability gradient track [math] and the initial droplet diameter d0) of a wettability gradient track laid on a superhydrophobic background represents wettability confinement. A lower value of [math]* represents higher wettability confinement. Droplet behavior changes for different wettability confinements and gradients of the track. It is found that droplet velocity is a function of the wettability confinement and the gradient; droplet transport velocity is maximum for [math]* = 0.8. Higher confinement ([math]* < 0.8) leads to a significant reduction in droplet velocity. Droplet transport characteristics on hydrophilic–superhydrophilic, hydrophobic–superhydrophilic, and superhydrophobic–superhydrophilic tracks are studied. It is found that for a fixed length of the track, droplet velocity is maximum for the superhydrophobic–superhydrophilic track. A droplet transport regime is demonstrated for a wettability gradient track with different confinements, and it is found that the droplet is transported for wettability confinement [math]* > 0.6 irrespective of the wettability gradient of the track. These findings provide valuable insight into efficient droplet manipulation in microfluidic devices.

Categories: Latest papers in fluid mechanics