# Latest papers in fluid mechanics

### Splashing dynamics of a drop impact onto a deep liquid pool with moving film interface

Physics of Fluids, Volume 32, Issue 1, January 2020.

The impact of a drop onto a stagnant deep liquid pool results in jet formation in the splashing regime. The perturbations in the free surface alter the impact conditions and change the splash dynamics. We present the simulations of the water drop impact onto a deep liquid pool with a moving free surface. Occurrence of the asymmetric crater profile and bending of the central jet toward the flow direction of the free surface are observed. The inclination of the jet increased with an increase in inertia of the moving liquid surface. A secondary droplet pinched-off from the tip of the jet, and the volume of this droplet increased with an increase in the inclination of the jet.

The impact of a drop onto a stagnant deep liquid pool results in jet formation in the splashing regime. The perturbations in the free surface alter the impact conditions and change the splash dynamics. We present the simulations of the water drop impact onto a deep liquid pool with a moving free surface. Occurrence of the asymmetric crater profile and bending of the central jet toward the flow direction of the free surface are observed. The inclination of the jet increased with an increase in inertia of the moving liquid surface. A secondary droplet pinched-off from the tip of the jet, and the volume of this droplet increased with an increase in the inclination of the jet.

Categories: Latest papers in fluid mechanics

### Impact of surfactant addition on non-Newtonian fluid behavior during viscous fingering in Hele-Shaw cell

Physics of Fluids, Volume 32, Issue 1, January 2020.

We present an experimental study of viscous fingering caused by the displacement of an oil phase by non-Newtonian fluids such as Carbopol® 940 with and without surfactant (SDS) addition in a radial Hele-Shaw cell. When polymer solutions are injected, a variety of fingering patterns as a function of flow rate are observed, which differ from the classical Saffman-Taylor instability. We have shown that if the surfactant concentration locally decreases the interfacial tension, it also leads to a reduction of viscosity and hence results in an increasing impact on the capillary number. We found that surfactant-polymer solutions have wider fingers with increasing flow rates in contrast with Newtonian solutions. Our study also revealed that the relative finger width of both non-Newtonian experiments with and without the surfactant converge asymptotically to the same value. We think that this phenomenon is caused by the decrease in surfactant concentration in the vicinity of the tip as the finger is growing so that the shear-thinning features of polymer prevail at long time.

We present an experimental study of viscous fingering caused by the displacement of an oil phase by non-Newtonian fluids such as Carbopol® 940 with and without surfactant (SDS) addition in a radial Hele-Shaw cell. When polymer solutions are injected, a variety of fingering patterns as a function of flow rate are observed, which differ from the classical Saffman-Taylor instability. We have shown that if the surfactant concentration locally decreases the interfacial tension, it also leads to a reduction of viscosity and hence results in an increasing impact on the capillary number. We found that surfactant-polymer solutions have wider fingers with increasing flow rates in contrast with Newtonian solutions. Our study also revealed that the relative finger width of both non-Newtonian experiments with and without the surfactant converge asymptotically to the same value. We think that this phenomenon is caused by the decrease in surfactant concentration in the vicinity of the tip as the finger is growing so that the shear-thinning features of polymer prevail at long time.

Categories: Latest papers in fluid mechanics

### Analysis of granular rheology in a quasi-two-dimensional slow flow by means of discrete element method based simulations

Physics of Fluids, Volume 32, Issue 1, January 2020.

The steady flow of spherical particles in a rectangular bin is studied using the discrete element method for different flow rates of the particles from the bin in the slow flow regime. The flow has two nonzero velocity components and is more complex than the widely studied unidirectional shear flows. The objective of the study is to characterize, in detail, the local rheology of the flowing material. The flow is shown to be of nearly constant density, with a symmetric stress tensor and the principal directions of the stress and rate of strain tensors being nearly colinear. The local rheology is analyzed using a coordinate transformation which enables direct computation of the viscosity and components of the pressure assuming the granular material to be a generalized Newtonian fluid. The scaled viscosity, fluctuation velocity, and volume fraction are shown to follow power law relations with the inertial number, a scaled shear rate, and data for different flow rates collapse to a single curve in each case. Results for flow of the particles on an inclined surface, presented for comparison, are similar to those for the bin flow but with a lower viscosity and a higher solid fraction due to layering of the particles. The in plane normal stresses are nearly equal and slightly larger than the third component. All three normal stresses correlate well with the corresponding fluctuation velocity components. Based on the empirical correlations obtained, a continuum model is presented for computation of granular flows.

The steady flow of spherical particles in a rectangular bin is studied using the discrete element method for different flow rates of the particles from the bin in the slow flow regime. The flow has two nonzero velocity components and is more complex than the widely studied unidirectional shear flows. The objective of the study is to characterize, in detail, the local rheology of the flowing material. The flow is shown to be of nearly constant density, with a symmetric stress tensor and the principal directions of the stress and rate of strain tensors being nearly colinear. The local rheology is analyzed using a coordinate transformation which enables direct computation of the viscosity and components of the pressure assuming the granular material to be a generalized Newtonian fluid. The scaled viscosity, fluctuation velocity, and volume fraction are shown to follow power law relations with the inertial number, a scaled shear rate, and data for different flow rates collapse to a single curve in each case. Results for flow of the particles on an inclined surface, presented for comparison, are similar to those for the bin flow but with a lower viscosity and a higher solid fraction due to layering of the particles. The in plane normal stresses are nearly equal and slightly larger than the third component. All three normal stresses correlate well with the corresponding fluctuation velocity components. Based on the empirical correlations obtained, a continuum model is presented for computation of granular flows.

Categories: Latest papers in fluid mechanics

### On the transition behavior of laminar flow through and around a multi-cylinder array

Physics of Fluids, Volume 32, Issue 1, January 2020.

We numerically investigated the transitional behavior of two-dimensional laminar flows through and around a square array of 100 circular cylinders. The solid fraction of the array ϕ ranged from 0.007 85 to 0.661 and the Reynolds number Re (based on the free-stream velocity and the side length of the array) varied from 40 to 200. Globally, the first transition appears at the onset of vortex shedding, where the critical Reynolds number Recr is estimated from the Stuart-Landau equation. The results show that Recr ranges from 40 to ∼45 for the investigated range of ϕ. It is found that Recr increases quadratically with [math] and the critical Reynolds number for an individual cylinder (Rdcr) increases linearly with [math]. The subsequent transitions largely depend on ϕ, as revealed from the total drag and lift coefficients, Strouhal number, and the instantaneous vorticity field. For sufficiently small ϕ at high Re, the global vortex shedding is suppressed due to the weakened interaction between cylinders in the array. Several more cases with ϕ of 0.007 85 for Re between 400 and 4000 are also calculated to visualize the suppression behavior. The global transition behaviors are closely related to the secondary frequency (SF) observed from the power spectra of the local velocity. It is highly possible that the SF results from the cylinder interaction in the array. The local instabilities induced by cylinder interactions would promote the onset of global vortex shedding at small Re. Also, the local instabilities still exist even though the global vortex shedding is suppressed at large Re.

We numerically investigated the transitional behavior of two-dimensional laminar flows through and around a square array of 100 circular cylinders. The solid fraction of the array ϕ ranged from 0.007 85 to 0.661 and the Reynolds number Re (based on the free-stream velocity and the side length of the array) varied from 40 to 200. Globally, the first transition appears at the onset of vortex shedding, where the critical Reynolds number Recr is estimated from the Stuart-Landau equation. The results show that Recr ranges from 40 to ∼45 for the investigated range of ϕ. It is found that Recr increases quadratically with [math] and the critical Reynolds number for an individual cylinder (Rdcr) increases linearly with [math]. The subsequent transitions largely depend on ϕ, as revealed from the total drag and lift coefficients, Strouhal number, and the instantaneous vorticity field. For sufficiently small ϕ at high Re, the global vortex shedding is suppressed due to the weakened interaction between cylinders in the array. Several more cases with ϕ of 0.007 85 for Re between 400 and 4000 are also calculated to visualize the suppression behavior. The global transition behaviors are closely related to the secondary frequency (SF) observed from the power spectra of the local velocity. It is highly possible that the SF results from the cylinder interaction in the array. The local instabilities induced by cylinder interactions would promote the onset of global vortex shedding at small Re. Also, the local instabilities still exist even though the global vortex shedding is suppressed at large Re.

Categories: Latest papers in fluid mechanics

### Transition to chaos in the cylinder wake through the Mode C flow

Physics of Fluids, Volume 32, Issue 1, January 2020.

The evolution of Mode C wake characteristics with the Reynolds number (Re) for Re up to 400 is investigated numerically. The Mode C wake instability is generated by placing a small wire in the near wake of a main circular cylinder. This setup ensures that the wake is unstable to Mode C only (without potential mode interactions), as demonstrated by Floquet stability analysis. Based on three-dimensional direct numerical simulations, three evolution regimes are identified for the fully developed Mode C flow. In the uniform periodic regime (Re = 166.4–210), the Mode C structure is uniformly distributed along the spanwise direction. The flow structure is 2T-periodic (T being the vortex shedding period) but retains a spatiotemporal symmetry every 1T. In the nonuniform periodic regime (Re = 220–230), the slightly nonuniform Mode C structure remains 2T-periodic at Re = 220 but undergoes a period quadrupling to 4T-periodic at Re = 230 before transitioning to chaos. In the chaotic regime (Re ≥ 240), the flow loses periodicity and becomes increasingly chaotic with increasing Re. The progressive wake transition to chaos is found to originate from the instability in the braid shear layer region through the uneven growth in strength and the consequent nonuniformity of the Mode C streamwise vortices. The wake transitions to chaos through the routes of Mode C and Mode B (for an isolated circular/square cylinder) are compared.

The evolution of Mode C wake characteristics with the Reynolds number (Re) for Re up to 400 is investigated numerically. The Mode C wake instability is generated by placing a small wire in the near wake of a main circular cylinder. This setup ensures that the wake is unstable to Mode C only (without potential mode interactions), as demonstrated by Floquet stability analysis. Based on three-dimensional direct numerical simulations, three evolution regimes are identified for the fully developed Mode C flow. In the uniform periodic regime (Re = 166.4–210), the Mode C structure is uniformly distributed along the spanwise direction. The flow structure is 2T-periodic (T being the vortex shedding period) but retains a spatiotemporal symmetry every 1T. In the nonuniform periodic regime (Re = 220–230), the slightly nonuniform Mode C structure remains 2T-periodic at Re = 220 but undergoes a period quadrupling to 4T-periodic at Re = 230 before transitioning to chaos. In the chaotic regime (Re ≥ 240), the flow loses periodicity and becomes increasingly chaotic with increasing Re. The progressive wake transition to chaos is found to originate from the instability in the braid shear layer region through the uneven growth in strength and the consequent nonuniformity of the Mode C streamwise vortices. The wake transitions to chaos through the routes of Mode C and Mode B (for an isolated circular/square cylinder) are compared.

Categories: Latest papers in fluid mechanics

### Invited contributions from outstanding early career researchers

Physics of Fluids, Volume 32, Issue 1, January 2020.

Categories: Latest papers in fluid mechanics

### Special topic on food and fluids

Physics of Fluids, Volume 32, Issue 1, January 2020.

Categories: Latest papers in fluid mechanics

### Identification of trapping in a peristaltic flow: A new approach using dynamical system theory

Physics of Fluids, Volume 32, Issue 1, January 2020.

In this paper, we propose a new approach for the identification of characteristic peristaltic flow features such as “bolus” and “trapping.” Using dynamical system analysis, we relate the occurrence of a bolus to the existence of a center (an elliptic equilibrium point). Trapping occurs when centers exist under the wave crests along with a pair of saddles (hyperbolic equilibrium points) lying on the central line. For an augmented flow, centers form under the wave crests, whereas saddles lie above (below) the central line. The proposed approach works much better than the presently adopted approach in two ways: (1) it does not require random testing and (2) it characterizes the qualitative flow behavior for the complete range of parameter values. The literature is somewhat inconsistent with regard to the terminologies used for describing characteristic flow behaviors. We have addressed this issue by explicitly defining quantities such as “bolus,” “backward flow,” “trapping,” and “augmented flow.”

In this paper, we propose a new approach for the identification of characteristic peristaltic flow features such as “bolus” and “trapping.” Using dynamical system analysis, we relate the occurrence of a bolus to the existence of a center (an elliptic equilibrium point). Trapping occurs when centers exist under the wave crests along with a pair of saddles (hyperbolic equilibrium points) lying on the central line. For an augmented flow, centers form under the wave crests, whereas saddles lie above (below) the central line. The proposed approach works much better than the presently adopted approach in two ways: (1) it does not require random testing and (2) it characterizes the qualitative flow behavior for the complete range of parameter values. The literature is somewhat inconsistent with regard to the terminologies used for describing characteristic flow behaviors. We have addressed this issue by explicitly defining quantities such as “bolus,” “backward flow,” “trapping,” and “augmented flow.”

Categories: Latest papers in fluid mechanics

### Study on the dependence with the filling level of the sloshing wave pattern in a rectangular tank

Physics of Fluids, Volume 32, Issue 1, January 2020.

This work presents a study of the influence of the filling level on the wave pattern during a sloshing problem. To this end, a rectangular tank of aspect ratio 2:1 is mounted on a shake table subject to controlled external motions. A frequency sweep analysis is performed nearest to the primary resonance frequency using two different amplitudes of imposed motion and different water depths. The wave evolution is registered at certain control points. In particular, this work is devoted to identifying the effect of the filling level on the dynamics of the wave patterns, emphasizing the nonlinearities of the free surface and their dependence on the water depth. The free surface measurements are compared with those obtained from a fixed mesh finite element simulation of the Navier-Stokes equations. The free surface is tracked using a Lagrangian technique. The effect of the bottom boundary conditions on the wave pattern is also evaluated from these simulations. From the experiments, it is confirmed that maximum and minimum wave heights do not change for larger water depth, i.e., when deep water conditions are fulfilled. This fact is also reflected by the numerical results. The computed wave evolution satisfactorily matches the experimental data. In addition, analytical solutions obtained using a potential flow approach are also evaluated. They fail in the description of nonlinear responses, but their coefficients can be numerically or experimentally characterized to fit more realistic solutions.

This work presents a study of the influence of the filling level on the wave pattern during a sloshing problem. To this end, a rectangular tank of aspect ratio 2:1 is mounted on a shake table subject to controlled external motions. A frequency sweep analysis is performed nearest to the primary resonance frequency using two different amplitudes of imposed motion and different water depths. The wave evolution is registered at certain control points. In particular, this work is devoted to identifying the effect of the filling level on the dynamics of the wave patterns, emphasizing the nonlinearities of the free surface and their dependence on the water depth. The free surface measurements are compared with those obtained from a fixed mesh finite element simulation of the Navier-Stokes equations. The free surface is tracked using a Lagrangian technique. The effect of the bottom boundary conditions on the wave pattern is also evaluated from these simulations. From the experiments, it is confirmed that maximum and minimum wave heights do not change for larger water depth, i.e., when deep water conditions are fulfilled. This fact is also reflected by the numerical results. The computed wave evolution satisfactorily matches the experimental data. In addition, analytical solutions obtained using a potential flow approach are also evaluated. They fail in the description of nonlinear responses, but their coefficients can be numerically or experimentally characterized to fit more realistic solutions.

Categories: Latest papers in fluid mechanics

### Drag reduction by linear flexible polymers and its degradation in turbulent flow: A phenomenological explanation from chemical thermodynamics and kinetics

Physics of Fluids, Volume 32, Issue 1, January 2020.

Based on chemical thermodynamics and kinetics analysis, this work provides a phenomenological explanation of drag reduction and its degradation by linear flexible polymers. We propose that drag reduction happens due to the unstable thermodynamic environment created by the elongation of free polymers and aggregates, and degradation of drag reduction happens due to the unstable kinetic environment with the chain scission of the free polymer and aggregate. Experimental results from microscopic and macroscopic scales further validate the proposed theory. Fourier series is employed to explain the molecular weight distribution that happens in the drag reduction.

Based on chemical thermodynamics and kinetics analysis, this work provides a phenomenological explanation of drag reduction and its degradation by linear flexible polymers. We propose that drag reduction happens due to the unstable thermodynamic environment created by the elongation of free polymers and aggregates, and degradation of drag reduction happens due to the unstable kinetic environment with the chain scission of the free polymer and aggregate. Experimental results from microscopic and macroscopic scales further validate the proposed theory. Fourier series is employed to explain the molecular weight distribution that happens in the drag reduction.

Categories: Latest papers in fluid mechanics

### Vortex breakdown in the lower fluid of two-fluid swirling flow

Physics of Fluids, Volume 32, Issue 1, January 2020.

This paper describes the first experimental evidence of the vortex breakdown development in the lower fluid in a sealed vertical cylindrical container in which two immiscible fluids circulate, driven by a rotating lid. The lower fluid is water, and the upper fluid is sunflower oil. In both fluids, the rotation generates centrifugal meridional circulations separated by a thin anticentrifugal circulation layer attached to the interface from below. An advanced technique of particle image velocimetry and proper laser illumination allows for the measurement of velocity and recognition of the patterns of flow in oil and water. As the rotation speeds up, a tornadolike swirling ascending jet forms near the axis-bottom intersection. A circulation cell (vortex-breakdown bubble, VBB) then emerges near the center of the water domain, approaches the bottom, and disappears. This scenario of the appearance and disappearance of the VBB is similar to that occurring in a single-fluid flow and in the upper fluid of a two-fluid flow.

This paper describes the first experimental evidence of the vortex breakdown development in the lower fluid in a sealed vertical cylindrical container in which two immiscible fluids circulate, driven by a rotating lid. The lower fluid is water, and the upper fluid is sunflower oil. In both fluids, the rotation generates centrifugal meridional circulations separated by a thin anticentrifugal circulation layer attached to the interface from below. An advanced technique of particle image velocimetry and proper laser illumination allows for the measurement of velocity and recognition of the patterns of flow in oil and water. As the rotation speeds up, a tornadolike swirling ascending jet forms near the axis-bottom intersection. A circulation cell (vortex-breakdown bubble, VBB) then emerges near the center of the water domain, approaches the bottom, and disappears. This scenario of the appearance and disappearance of the VBB is similar to that occurring in a single-fluid flow and in the upper fluid of a two-fluid flow.

Categories: Latest papers in fluid mechanics

### Efficient microextraction process exploiting spontaneous interfacial convection driven by Marangoni and electric field induced instability: A computational fluid dynamics study

Physics of Fluids, Volume 32, Issue 1, January 2020.

The present study focuses on the component transfer from one liquid phase to another liquid phase, commonly known as the extraction process, performed in a microchannel in the presence of spontaneous interfacial convection, driven by either an interfacial tension gradient or an applied external electric field. Marangoni instability occurs as a result of a lateral gradient of interfacial tension existing along the interface of the two fluids. Nonequilibrium phenomena associated with factors such as temperature imbalance, a nonuniform distribution of surface-active components at the interface, evaporation, etc. can lead to the interfacial Marangoni instability. In the present study, first, we have explored temperature gradient driven Marangoni instability, which deforms the interface with significant acceleration and induces local convective mass transfer along with the conventional diffusion mode. Next, we have explored the same phenomenon in the presence of an external electric field, which can also deform the liquid-liquid interface almost instantaneously to a considerable extent. The relative strength of the mass transfer rate for different cases, such as temperature driven instability, in the presence of uniform and nonuniform electric fields has been reported in detail. It has also been observed that, due to the larger mass transfer area, the annular flow offers an enhanced rate of mass transfer compared to the stratified flow. Additionally, this article reports that the nonuniform electric field could influence the process of interfacial instability more strongly compared to the uniform electric field. The effect of the nonuniform electric field with different spatial periodicity on the extraction process has been studied in detail.

The present study focuses on the component transfer from one liquid phase to another liquid phase, commonly known as the extraction process, performed in a microchannel in the presence of spontaneous interfacial convection, driven by either an interfacial tension gradient or an applied external electric field. Marangoni instability occurs as a result of a lateral gradient of interfacial tension existing along the interface of the two fluids. Nonequilibrium phenomena associated with factors such as temperature imbalance, a nonuniform distribution of surface-active components at the interface, evaporation, etc. can lead to the interfacial Marangoni instability. In the present study, first, we have explored temperature gradient driven Marangoni instability, which deforms the interface with significant acceleration and induces local convective mass transfer along with the conventional diffusion mode. Next, we have explored the same phenomenon in the presence of an external electric field, which can also deform the liquid-liquid interface almost instantaneously to a considerable extent. The relative strength of the mass transfer rate for different cases, such as temperature driven instability, in the presence of uniform and nonuniform electric fields has been reported in detail. It has also been observed that, due to the larger mass transfer area, the annular flow offers an enhanced rate of mass transfer compared to the stratified flow. Additionally, this article reports that the nonuniform electric field could influence the process of interfacial instability more strongly compared to the uniform electric field. The effect of the nonuniform electric field with different spatial periodicity on the extraction process has been studied in detail.

Categories: Latest papers in fluid mechanics

### Experimental investigation of turbulent Rayleigh-Bénard convection of water in a cylindrical cell: The Prandtl number effects for Pr [math] 1

Physics of Fluids, Volume 32, Issue 1, January 2020.

We report an experimental study of turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio unity, focusing on the effects of the Prandtl number (Pr). Purified water was used as the convecting fluid. Five different Pr between 3.58 and 9.40 were achieved by changing the mean temperature of water, and the measurements were carried out over the Rayleigh number range 2.63 × 108 ≤ Ra ≤ 3.89 × 1010. Over the present parameter range, the measured Nusselt number Nu is found to scale as Nu ∼ Raβ with β = 0.30 and to be independent of Pr. Based on the oscillation period of the measured temperature, the Reynolds number Re scales as Re ∼ Ra0.47Pr−0.72. The local temperature fluctuations at the cell center and near the cell’s sidewall were measured, and their relations with Ra and Pr were studied. Our results further reveal that the non-Oberbeck-Boussinesq effects of water have a relatively small influence on the measured scaling relation Nu ∼ Raβ.

We report an experimental study of turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio unity, focusing on the effects of the Prandtl number (Pr). Purified water was used as the convecting fluid. Five different Pr between 3.58 and 9.40 were achieved by changing the mean temperature of water, and the measurements were carried out over the Rayleigh number range 2.63 × 108 ≤ Ra ≤ 3.89 × 1010. Over the present parameter range, the measured Nusselt number Nu is found to scale as Nu ∼ Raβ with β = 0.30 and to be independent of Pr. Based on the oscillation period of the measured temperature, the Reynolds number Re scales as Re ∼ Ra0.47Pr−0.72. The local temperature fluctuations at the cell center and near the cell’s sidewall were measured, and their relations with Ra and Pr were studied. Our results further reveal that the non-Oberbeck-Boussinesq effects of water have a relatively small influence on the measured scaling relation Nu ∼ Raβ.

Categories: Latest papers in fluid mechanics

### Evolution of the flow structures in an elevated jet in crossflow

Physics of Fluids, Volume 32, Issue 1, January 2020.

The characteristic flow features of an elevated square jet in crossflow (EJICF) are studied numerically using large eddy simulation. The effect of jet to crossflow velocity ratio, also called velocity ratio (VR), on the flow field of an elevated jet in crossflow (EJICF) is investigated. All the computations are carried out at a Reynolds number (Re) of 20 000, based on the outer width of the stack (d) and free stream crossflow velocity (U∞), for four different velocity ratios (VR), namely, 0.5, 1.0, 1.5 and 2.0. The stack used in this study has an aspect ratio h/d = 7. The shear-improved Smagorinsky model has been used to account for the subgrid scale stress while solving the filtered three-dimensional unsteady Navier-Stokes equations. The modes of shedding in the stack wake are analyzed using both instantaneous and phase-averaged data. It is found that at a low jet to crossflow velocity ratio (VR = 0.5), the stack wake exhibits two different modes of shedding, symmetric and antisymmetric, similar to the wake of a wall mounted finite-size cylinder. At higher velocity ratios (VR ≥ 1), the stack wake shows the presence of only antisymmetric modes of shedding. It is also found that velocity ratio (VR) has a profound effect on the source of vorticity of the jet shear layer structures near the upwind side. At VR = 0.5, the upstream sides of the jet shear layer structures are found to draw their vortices from the outer surface of the stack boundary layer. At higher VR, they seem to be fed by the vorticity of the boundary layer developed on the inner wall surface of the stack. Both jet vortices and stack wake vortices are found to be present in the jet wake, and the shedding frequency of both the jet wake and the stack wake is found to be same. The spatial evolution of the counter-rotating vortex pair in the case of an EJICF is found to be similar to that of a JICF.

The characteristic flow features of an elevated square jet in crossflow (EJICF) are studied numerically using large eddy simulation. The effect of jet to crossflow velocity ratio, also called velocity ratio (VR), on the flow field of an elevated jet in crossflow (EJICF) is investigated. All the computations are carried out at a Reynolds number (Re) of 20 000, based on the outer width of the stack (d) and free stream crossflow velocity (U∞), for four different velocity ratios (VR), namely, 0.5, 1.0, 1.5 and 2.0. The stack used in this study has an aspect ratio h/d = 7. The shear-improved Smagorinsky model has been used to account for the subgrid scale stress while solving the filtered three-dimensional unsteady Navier-Stokes equations. The modes of shedding in the stack wake are analyzed using both instantaneous and phase-averaged data. It is found that at a low jet to crossflow velocity ratio (VR = 0.5), the stack wake exhibits two different modes of shedding, symmetric and antisymmetric, similar to the wake of a wall mounted finite-size cylinder. At higher velocity ratios (VR ≥ 1), the stack wake shows the presence of only antisymmetric modes of shedding. It is also found that velocity ratio (VR) has a profound effect on the source of vorticity of the jet shear layer structures near the upwind side. At VR = 0.5, the upstream sides of the jet shear layer structures are found to draw their vortices from the outer surface of the stack boundary layer. At higher VR, they seem to be fed by the vorticity of the boundary layer developed on the inner wall surface of the stack. Both jet vortices and stack wake vortices are found to be present in the jet wake, and the shedding frequency of both the jet wake and the stack wake is found to be same. The spatial evolution of the counter-rotating vortex pair in the case of an EJICF is found to be similar to that of a JICF.

Categories: Latest papers in fluid mechanics

### Experimental investigation of interactions between turbulent cylinder wake and spherical shock wave

Physics of Fluids, Volume 32, Issue 1, January 2020.

Interactions between a spherical shock wave and a turbulent cylinder wake are studied with wind tunnel experiments. The shock wave is generated outside the wake and propagates across the turbulent wake. Instantaneous streamwise velocity is measured on the wake centerline while peak overpressure of the shock wave is measured outside the wake after the shock wave has passed across the wake. The experiments are performed for various conditions of the cylinder wake to investigate the influences of the root-mean-squared (rms) velocity fluctuation and of the length of the turbulent region through which the shock wave propagates. The velocity fluctuation opposite to the shock propagation direction is positively correlated with the peak-overpressure fluctuation. The mean peak overpressure decreases after the shock wave propagates in the wake. These relations between velocity and peak overpressure are explained by the shock-surface deformation, where the peak overpressure is increased and decreased, respectively, for the shock surfaces with concave and convex shapes in relation to the shock propagation direction. The correlation coefficients between the velocity and peak-overpressure fluctuations and the rms peak-overpressure fluctuation increase with the rms velocity fluctuation. The rms peak-overpressure fluctuation becomes independent of the turbulent length on the shock ray once the shock wave has propagated through a sufficiently long turbulent region. The peak-overpressure fluctuation has a probability density function (PDF) close to a Gaussian shape even though the PDF of velocity fluctuations in the wake is negatively skewed.

Interactions between a spherical shock wave and a turbulent cylinder wake are studied with wind tunnel experiments. The shock wave is generated outside the wake and propagates across the turbulent wake. Instantaneous streamwise velocity is measured on the wake centerline while peak overpressure of the shock wave is measured outside the wake after the shock wave has passed across the wake. The experiments are performed for various conditions of the cylinder wake to investigate the influences of the root-mean-squared (rms) velocity fluctuation and of the length of the turbulent region through which the shock wave propagates. The velocity fluctuation opposite to the shock propagation direction is positively correlated with the peak-overpressure fluctuation. The mean peak overpressure decreases after the shock wave propagates in the wake. These relations between velocity and peak overpressure are explained by the shock-surface deformation, where the peak overpressure is increased and decreased, respectively, for the shock surfaces with concave and convex shapes in relation to the shock propagation direction. The correlation coefficients between the velocity and peak-overpressure fluctuations and the rms peak-overpressure fluctuation increase with the rms velocity fluctuation. The rms peak-overpressure fluctuation becomes independent of the turbulent length on the shock ray once the shock wave has propagated through a sufficiently long turbulent region. The peak-overpressure fluctuation has a probability density function (PDF) close to a Gaussian shape even though the PDF of velocity fluctuations in the wake is negatively skewed.

Categories: Latest papers in fluid mechanics

### Experimental study of inertia-based passive flexibility of a heaving and pitching airfoil operating in the energy harvesting regime

Physics of Fluids, Volume 32, Issue 1, January 2020.

The effects of passive, inertia-induced surface flexibility at the leading and trailing edges of an oscillating airfoil energy harvester are investigated experimentally at reduced frequencies of k = fc/U∞ = 0.10, 0.14, and 0.18. Wind tunnel experiments are conducted using phase-resolved, two-component particle image velocimetry to understand the underlying flow physics, as well as to obtain force and pitching moment estimates using the vortex-impulse theory. Results are obtained for leading and trailing edge flexibility separately. It is shown that both forms of flexibility may alter the leading edge vortex inception and detachment time scales, as well as the growth rate of the circulation. In addition, surface flexibility may also trigger the generation of secondary vortical structures and suppress the formation of trailing edge vortices. The total energy harvesting efficiency is decomposed into contributions of heaving and pitching motions. Relative to the rigid airfoil, the flexible leading and trailing edge segments are shown to increase the energy harvesting efficiency by approximately 17% and 25%, respectively. However, both the flexible leading and trailing edge airfoils operate most efficiently at k = 0.18, whereas the peak efficiency of the rigid airfoil occurs at k = 0.14. It is shown that the flexible leading and trailing edge airfoils enhance the heaving contribution to the total efficiency at k = 0.18 and the negative contribution of the pitching motion at high reduced frequencies can be alleviated by using a flexible trailing edge.

The effects of passive, inertia-induced surface flexibility at the leading and trailing edges of an oscillating airfoil energy harvester are investigated experimentally at reduced frequencies of k = fc/U∞ = 0.10, 0.14, and 0.18. Wind tunnel experiments are conducted using phase-resolved, two-component particle image velocimetry to understand the underlying flow physics, as well as to obtain force and pitching moment estimates using the vortex-impulse theory. Results are obtained for leading and trailing edge flexibility separately. It is shown that both forms of flexibility may alter the leading edge vortex inception and detachment time scales, as well as the growth rate of the circulation. In addition, surface flexibility may also trigger the generation of secondary vortical structures and suppress the formation of trailing edge vortices. The total energy harvesting efficiency is decomposed into contributions of heaving and pitching motions. Relative to the rigid airfoil, the flexible leading and trailing edge segments are shown to increase the energy harvesting efficiency by approximately 17% and 25%, respectively. However, both the flexible leading and trailing edge airfoils operate most efficiently at k = 0.18, whereas the peak efficiency of the rigid airfoil occurs at k = 0.14. It is shown that the flexible leading and trailing edge airfoils enhance the heaving contribution to the total efficiency at k = 0.18 and the negative contribution of the pitching motion at high reduced frequencies can be alleviated by using a flexible trailing edge.

Categories: Latest papers in fluid mechanics

### Turbulence modulation by settling inertial aerosols in Eulerian-Eulerian and Eulerian-Lagrangian simulations of homogeneously sheared turbulence

Author(s): M. Houssem Kasbaoui

When subject to strong shear, settling particles dispersed at semidilute concentrations may modulate the suspending flow significantly, in a way that enhances or attenuates turbulence. The modulation is enabled by the appearance of clusters and void fraction bubbles in the particle phase.

[Phys. Rev. Fluids 4, 124308] Published Tue Dec 31, 2019

Categories: Latest papers in fluid mechanics

### Spontaneous aggregation of bovine milk casein micelles: Ultra-small angle x-ray scattering and mathematical modeling

Physics of Fluids, Volume FAF2019, Issue 1, December 2019.

We have used Ultra Small Angle X-ray Scattering (USAXS) and mathematical models to study seemingly-spontaneous aggregation structures in two pasteurized bovine milks. Although extensive studies of casein micelles and their aggregation have been carried out, few have been done to numerically characterize submicron structures to micron-scale structures. We measured the USAXS intensity, I(q), as a function of the scattering vector magnitude, q, for commercial pasteurized skim milk and nonhomogenized whole milk at two temperatures, 7 °C and 45 °C. We observed broad peaks, reported previously to be related to casein micelles, centered at q ≈ 2 × 10−2 Å−1 and at q ≈ 9 × 10−2 Å−1. At lower q values, log I(q) displayed a behavior characteristic of aggregation manifested for a slope in the region 3–7 × 10−4 Å−1 < q < 4 × 10−3 Å−1. This behavior appeared in the absence of (a) chymosin, (b) any change in pH or CaCl2 concentration, and (c) temperature changes. We introduced a model of milk and used computer simulations to investigate consequences of casein micelles possessing surface areas lacking the water-soluble components of κ-casein proteins. These components exist to provide stability against aggregation to the casein micelles. We propose that bovine casein micelles spontaneously formed 1-dimensional aggregates.

We have used Ultra Small Angle X-ray Scattering (USAXS) and mathematical models to study seemingly-spontaneous aggregation structures in two pasteurized bovine milks. Although extensive studies of casein micelles and their aggregation have been carried out, few have been done to numerically characterize submicron structures to micron-scale structures. We measured the USAXS intensity, I(q), as a function of the scattering vector magnitude, q, for commercial pasteurized skim milk and nonhomogenized whole milk at two temperatures, 7 °C and 45 °C. We observed broad peaks, reported previously to be related to casein micelles, centered at q ≈ 2 × 10−2 Å−1 and at q ≈ 9 × 10−2 Å−1. At lower q values, log I(q) displayed a behavior characteristic of aggregation manifested for a slope in the region 3–7 × 10−4 Å−1 < q < 4 × 10−3 Å−1. This behavior appeared in the absence of (a) chymosin, (b) any change in pH or CaCl2 concentration, and (c) temperature changes. We introduced a model of milk and used computer simulations to investigate consequences of casein micelles possessing surface areas lacking the water-soluble components of κ-casein proteins. These components exist to provide stability against aggregation to the casein micelles. We propose that bovine casein micelles spontaneously formed 1-dimensional aggregates.

Categories: Latest papers in fluid mechanics

### Surface rheological measurements of isolated food foam systems

Physics of Fluids, Volume FAF2019, Issue 1, December 2019.

Liquid foams represent a key component to a vast range of food industry products, from ice creams to the crema on coffee. Longevity of these foams is a highly desirable attribute; however, in order for foam stability to be effectively controlled, a better understanding of the interdependence of the bulk liquid and air-liquid interfacial rheologies is required. This study follows an increasing trend in experimental investigations made of isolated foam structures at the microscale, where the bulk and surface dynamics of a single foam liquid channel can be accurately assessed. Isolated foam channels with adjoining nodes were studied for aqueous solutions of four food grade surfactants. Existing observations of distortions to sodium dodecyl sulphate channel geometries were confirmed for solutions of Tween 20 (T20) and Tween 80 (T80) and were well described by the theory presented here. Moreover, previously unseen distortions to liquid channels were observed for polymeric surfactant systems (hydroxypropyl methylcellulose and hydrolyzed pea protein blend), which were proposed to result from their high surface viscosities. The apparent surface viscosities, μs, of surfactants tested here ranged from high (10 g/s < μs < 10−3 g/s) for polymeric surfactants to very low (10−10 g/s < μs < 10−8 g/s) for Tweens, clearly demarking the regimes of viscous and inertial dominant flows, respectively. It is recommended that further work seeks to investigate the finding of a strong correlation between μs and channel surface tension, γ, for soluble surfactant systems, which could explain the apparent non-Newtonian values of μs that were consistently measured here.

Liquid foams represent a key component to a vast range of food industry products, from ice creams to the crema on coffee. Longevity of these foams is a highly desirable attribute; however, in order for foam stability to be effectively controlled, a better understanding of the interdependence of the bulk liquid and air-liquid interfacial rheologies is required. This study follows an increasing trend in experimental investigations made of isolated foam structures at the microscale, where the bulk and surface dynamics of a single foam liquid channel can be accurately assessed. Isolated foam channels with adjoining nodes were studied for aqueous solutions of four food grade surfactants. Existing observations of distortions to sodium dodecyl sulphate channel geometries were confirmed for solutions of Tween 20 (T20) and Tween 80 (T80) and were well described by the theory presented here. Moreover, previously unseen distortions to liquid channels were observed for polymeric surfactant systems (hydroxypropyl methylcellulose and hydrolyzed pea protein blend), which were proposed to result from their high surface viscosities. The apparent surface viscosities, μs, of surfactants tested here ranged from high (10 g/s < μs < 10−3 g/s) for polymeric surfactants to very low (10−10 g/s < μs < 10−8 g/s) for Tweens, clearly demarking the regimes of viscous and inertial dominant flows, respectively. It is recommended that further work seeks to investigate the finding of a strong correlation between μs and channel surface tension, γ, for soluble surfactant systems, which could explain the apparent non-Newtonian values of μs that were consistently measured here.

Categories: Latest papers in fluid mechanics

### Influence of flowing fluid property through an elastic tube on various deformations along the tube length

Physics of Fluids, Volume FAF2019, Issue 1, December 2019.

The study of fluid flow characteristics in collapsible elastic tubes is useful to understand biofluid mechanics encountered in the human body. The research work presented here is aimed at thoroughly investigating the influence of both Newtonian and/or non-Newtonian fluids (low and high shear thinning) during steady flow through an elastic tube on various tube deformations, which enables understanding of the interaction between wall motion, fluid flow, and intestinal transmembrane mass transfer as a crucial contribution to a mechanistic understanding of bioaccessibility/bioavailability. It is observed that for a given steady volume flow rate, the tube is buckled from an elliptical shape to a line or area contacted two lobes as the critical external pressure is increased. The downstream transmural pressure is found to get more negative than that at the upstream as the outlet pressure decreased due to stronger tube collapse resulting in a reduced cross-sectional area. The experimental results depict that the tube cross-sectional area decreased by only about a factor of one for PEG (polyethylene glycol) and about a factor of six for both CMC (carboxymethyl cellulose) and PAA (polyacrylamide) from the undeformed one under an applied external pressure of 105 mbar. The corresponding maximum velocity increased by a factor of two during steady flow of shear-thinning fluids. The shear-thinning behavior of both CMC and PAA solutions is clearly observed at a constant flow rate of 17 ml/s as the tube cross-sectional area decreased due to an increase in compressive transmural pressure. In addition, the viscosity of PAA is drastically decreased due to its high shear-thinning behavior than that of the CMC under the same applied external pressure.

The study of fluid flow characteristics in collapsible elastic tubes is useful to understand biofluid mechanics encountered in the human body. The research work presented here is aimed at thoroughly investigating the influence of both Newtonian and/or non-Newtonian fluids (low and high shear thinning) during steady flow through an elastic tube on various tube deformations, which enables understanding of the interaction between wall motion, fluid flow, and intestinal transmembrane mass transfer as a crucial contribution to a mechanistic understanding of bioaccessibility/bioavailability. It is observed that for a given steady volume flow rate, the tube is buckled from an elliptical shape to a line or area contacted two lobes as the critical external pressure is increased. The downstream transmural pressure is found to get more negative than that at the upstream as the outlet pressure decreased due to stronger tube collapse resulting in a reduced cross-sectional area. The experimental results depict that the tube cross-sectional area decreased by only about a factor of one for PEG (polyethylene glycol) and about a factor of six for both CMC (carboxymethyl cellulose) and PAA (polyacrylamide) from the undeformed one under an applied external pressure of 105 mbar. The corresponding maximum velocity increased by a factor of two during steady flow of shear-thinning fluids. The shear-thinning behavior of both CMC and PAA solutions is clearly observed at a constant flow rate of 17 ml/s as the tube cross-sectional area decreased due to an increase in compressive transmural pressure. In addition, the viscosity of PAA is drastically decreased due to its high shear-thinning behavior than that of the CMC under the same applied external pressure.

Categories: Latest papers in fluid mechanics