# 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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### Effects of flexibility and entanglement of sodium hyaluronate in solutions on the entry flow in micro abrupt contraction-expansion channels

Physics of Fluids, Volume 31, Issue 7, July 2019.

In this study, the effects of polymer flexibility and entanglement on elastic instability were investigated by observing sodium hyaluronate (hyaluronic acid sodium salt, Na-HA) solution in planar abrupt contraction-expansion microchannels. As the rigidity of Na-HA depends on the ionic strength of a solvent, Na-HA was dissolved in water and phosphate buffered saline with concentrations from 0.15 wt. % to 0.45 wt. %. The rheological properties were measured and analyzed to detect the Na-HA overlap and entanglement concentrations. The flow regimes of the Na-HA solutions in several planar abrupt contraction-expansion channels were characterized in the Reynolds number and Weissenberg number space. The effects of the solvent, solution concentration, and channel geometry on the elastic corner vortex growth curve and flow regimes characterized by the Weissenberg number were analyzed. It was found that the entanglement of Na-HA in the solution is a more dominant factor affecting the flow regimes than the solution relaxation time and polymer rigidity.

In this study, the effects of polymer flexibility and entanglement on elastic instability were investigated by observing sodium hyaluronate (hyaluronic acid sodium salt, Na-HA) solution in planar abrupt contraction-expansion microchannels. As the rigidity of Na-HA depends on the ionic strength of a solvent, Na-HA was dissolved in water and phosphate buffered saline with concentrations from 0.15 wt. % to 0.45 wt. %. The rheological properties were measured and analyzed to detect the Na-HA overlap and entanglement concentrations. The flow regimes of the Na-HA solutions in several planar abrupt contraction-expansion channels were characterized in the Reynolds number and Weissenberg number space. The effects of the solvent, solution concentration, and channel geometry on the elastic corner vortex growth curve and flow regimes characterized by the Weissenberg number were analyzed. It was found that the entanglement of Na-HA in the solution is a more dominant factor affecting the flow regimes than the solution relaxation time and polymer rigidity.

Categories: Latest papers in fluid mechanics

### Contributions of hydrodynamic features of a swirling flow to thermoacoustic instabilities in a lean premixed swirl stabilized combustor

Physics of Fluids, Volume 31, Issue 7, July 2019.

A comprehensive study on influences of hydrodynamic features of a swirling flow on thermoacoustic instabilities in a swirl stabilized combustor is performed by using large eddy simulations along with the dynamically thickened flame combustion model. The governing equations in full compressible form are solved by an in-house developed high-order numerical solver. The combustor is simulated in six different equivalence ratios to assess effects of equivalence ratio on the contributions of hydrodynamic features in inducing thermoacoustic instabilities. The obtained results show that the combustor suffers from combustion instabilities at equivalence ratios of 0.55, 0.6, 0.75, and 0.8, while it is stable at the midrange equivalence ratios (0.65 and 0.7). The results indicate that the instabilities are the result of the lock-in mechanism between heat release fluctuations induced by hydrodynamic features and the mixed first tangential and quarter wave longitudinal mode of the combustor. Investigations are carried out to evaluate contributions of central and side recirculation zones, precessing vortex core, and coherent structures in heat release fluctuations. The results show that contributions of hydrodynamic features highly depend on the combustor operating condition. At low equivalence ratios (0.55 and 0.6), coherent structures and side and central recirculation zones are the key features to induce heat release fluctuations in phase with the acoustic perturbations, while at equivalence ratios of 0.75 and 0.8, coherent structures and precessing vortex core play the main role in inducing combustion instabilities.

A comprehensive study on influences of hydrodynamic features of a swirling flow on thermoacoustic instabilities in a swirl stabilized combustor is performed by using large eddy simulations along with the dynamically thickened flame combustion model. The governing equations in full compressible form are solved by an in-house developed high-order numerical solver. The combustor is simulated in six different equivalence ratios to assess effects of equivalence ratio on the contributions of hydrodynamic features in inducing thermoacoustic instabilities. The obtained results show that the combustor suffers from combustion instabilities at equivalence ratios of 0.55, 0.6, 0.75, and 0.8, while it is stable at the midrange equivalence ratios (0.65 and 0.7). The results indicate that the instabilities are the result of the lock-in mechanism between heat release fluctuations induced by hydrodynamic features and the mixed first tangential and quarter wave longitudinal mode of the combustor. Investigations are carried out to evaluate contributions of central and side recirculation zones, precessing vortex core, and coherent structures in heat release fluctuations. The results show that contributions of hydrodynamic features highly depend on the combustor operating condition. At low equivalence ratios (0.55 and 0.6), coherent structures and side and central recirculation zones are the key features to induce heat release fluctuations in phase with the acoustic perturbations, while at equivalence ratios of 0.75 and 0.8, coherent structures and precessing vortex core play the main role in inducing combustion instabilities.

Categories: Latest papers in fluid mechanics

### Sound waves in polarized fluids

Physics of Fluids, Volume 31, Issue 7, July 2019.

The speed of sound is known to depend only on the properties of the medium through which it travels. In this paper, we show that polarizing a dielectric fluid reduces the speed of sound waves in it. We also show that the reduction depends on the magnitude of the field. The striction force causing the slowing of sound in dielectric fluids is also present in a polarized ferrofluid. However, it is far too feeble to cause an observable effect.

The speed of sound is known to depend only on the properties of the medium through which it travels. In this paper, we show that polarizing a dielectric fluid reduces the speed of sound waves in it. We also show that the reduction depends on the magnitude of the field. The striction force causing the slowing of sound in dielectric fluids is also present in a polarized ferrofluid. However, it is far too feeble to cause an observable effect.

Categories: Latest papers in fluid mechanics

### Impact of tab location relative to the nozzle exit on the shock structure of a supersonic jet

Physics of Fluids, Volume 31, Issue 7, July 2019.

This paper presents an experimental study of a Mach 2.0 jet manipulated using rectangular tabs to understand the mixing enhancement at the overexpanded and perfectly expanded state of the jet. This paper also compares the mixing effectiveness of the tabs in comparison with the fluidic injection reported in our previous work [Kumar et al., “Empirical scaling analysis of supersonic jet control using steady fluidic injection,” Phys. Fluids 31(5), 056107 (2018)]. Tabs used in this investigation were rectangular strips of aspect ratio, AR, 2 (AR = length of the tab/width of the tab) and are positioned at 0De, 0.25De, 0.5De, and 0.95De (De is the nozzle exit diameter) downstream of the nozzle exit. Pitot pressure measurements were carried out along the jet centerline and in the radial directions to examine the supersonic core length ([math]) and jet spread, respectively. The jet stream has been visualized using the shadowgraph technique in the orthogonal planes of the manipulated jet. The mixing capability of the manipulated jet quantified based on the reduction in supersonic core length [math] strongly depends on the control technique and its location along the downstream direction. Three types of flow categories are identified, i.e., the “jet bifurcation,” “complex and strong shock-cell structure,” and “weak shock structure,” which depend on the tab location ([math]) and account for the jet mixing. The present study reveals that the tabs should be positioned downstream of the first shock crossover point which results in shorter core length and, hence, higher jet mixing. A conceptual model of the flow structure under control is proposed.

This paper presents an experimental study of a Mach 2.0 jet manipulated using rectangular tabs to understand the mixing enhancement at the overexpanded and perfectly expanded state of the jet. This paper also compares the mixing effectiveness of the tabs in comparison with the fluidic injection reported in our previous work [Kumar et al., “Empirical scaling analysis of supersonic jet control using steady fluidic injection,” Phys. Fluids 31(5), 056107 (2018)]. Tabs used in this investigation were rectangular strips of aspect ratio, AR, 2 (AR = length of the tab/width of the tab) and are positioned at 0De, 0.25De, 0.5De, and 0.95De (De is the nozzle exit diameter) downstream of the nozzle exit. Pitot pressure measurements were carried out along the jet centerline and in the radial directions to examine the supersonic core length ([math]) and jet spread, respectively. The jet stream has been visualized using the shadowgraph technique in the orthogonal planes of the manipulated jet. The mixing capability of the manipulated jet quantified based on the reduction in supersonic core length [math] strongly depends on the control technique and its location along the downstream direction. Three types of flow categories are identified, i.e., the “jet bifurcation,” “complex and strong shock-cell structure,” and “weak shock structure,” which depend on the tab location ([math]) and account for the jet mixing. The present study reveals that the tabs should be positioned downstream of the first shock crossover point which results in shorter core length and, hence, higher jet mixing. A conceptual model of the flow structure under control is proposed.

Categories: Latest papers in fluid mechanics

### Semi-empirical pressure loss model for viscous flow through high aspect ratio rectangular orifices

Physics of Fluids, Volume 31, Issue 7, July 2019.

A predictive model is developed for the pressure loss coefficient for a viscous flow through a rectangular orifice on a pipe-installed thick plate. The model is developed based on the 1-dimensional Navier-Stokes equation and an asymptotic increase in velocity modeled to have a direct relation with the flow convergence in the near-inlet region. Here, the flow velocity increases asymptotically from the steady mean upstream value to the orifice velocity. This phenomenon is represented by a convergence parameter, [math], used in the velocity transition model to quantify the length of the convergence zone. The static pressure drop is measured experimentally for varying orifice aspect ratio, AR, at creeping Reynolds numbers (0.01 ≤ Re ≤ 0.1). A significantly wider range of AR is covered (1 ≤ AR ≤ 250), compared to related works in the literature. Results show that the relative dominance of the convergence phenomenon is affected by AR. The maximum length of convergence is for the square orifice (AR = 1), as the flow experiences comparable convergence from all directions, whereas for higher AR, convergence becomes less dominant in one of the two midplanes of investigation. The loss coefficient thus decreases as AR increases. At constant Re, higher AR generally leads to higher pressure drop but lower values of the loss coefficient. The velocity gradient in the convergence zone is also determined as a function of AR and Re which verifies that lower AR takes a longer distance for the velocity transition due to increased convergence.

A predictive model is developed for the pressure loss coefficient for a viscous flow through a rectangular orifice on a pipe-installed thick plate. The model is developed based on the 1-dimensional Navier-Stokes equation and an asymptotic increase in velocity modeled to have a direct relation with the flow convergence in the near-inlet region. Here, the flow velocity increases asymptotically from the steady mean upstream value to the orifice velocity. This phenomenon is represented by a convergence parameter, [math], used in the velocity transition model to quantify the length of the convergence zone. The static pressure drop is measured experimentally for varying orifice aspect ratio, AR, at creeping Reynolds numbers (0.01 ≤ Re ≤ 0.1). A significantly wider range of AR is covered (1 ≤ AR ≤ 250), compared to related works in the literature. Results show that the relative dominance of the convergence phenomenon is affected by AR. The maximum length of convergence is for the square orifice (AR = 1), as the flow experiences comparable convergence from all directions, whereas for higher AR, convergence becomes less dominant in one of the two midplanes of investigation. The loss coefficient thus decreases as AR increases. At constant Re, higher AR generally leads to higher pressure drop but lower values of the loss coefficient. The velocity gradient in the convergence zone is also determined as a function of AR and Re which verifies that lower AR takes a longer distance for the velocity transition due to increased convergence.

Categories: Latest papers in fluid mechanics

### Vortex-induced vibrations of dual-step cylinders with different diameter ratios in laminar flows

Physics of Fluids, Volume 31, Issue 7, July 2019.

Vortex-induced vibrations of dual-step cylinders in laminar flows at the Reynolds number of 200 based on a larger diameter are investigated through three-dimensional direct numerical simulations. Four larger-to-smaller diameter ratios (D/d) of 4.0, 2.0, 1.43, and 1.19 are considered for the cylinder with a low mass ratio of 2. Numerical results reveal that D/d significantly influences vibration responses and the vortex shedding process. The case with D/d = 1.43 can effectively reduce vibration amplitudes. The wake vortices are shed in cellular patterns along the cylinder span, with a distinct frequency for each cell. A direct and “X-shaped” connection of wake vortex-shedding modes occurs between different vortex cells, and a loop connection appears between the same cell vortices. A new wake pattern entitled the “out-of-phase vortex shedding” is found downstream of the smaller cylinder at D/d = 2.0. This is manifested by the wake vortices not being shed at a fixed frequency and intensity. The essential reason for this phenomenon lies in a non-lock-in condition between the structural vibration and vortex shedding frequencies of the smaller cylinder. As D/d decreases, a coherence between vortex cells is enhanced, leading to a disappearance of the “out-of-phase vortex shedding.”

Vortex-induced vibrations of dual-step cylinders in laminar flows at the Reynolds number of 200 based on a larger diameter are investigated through three-dimensional direct numerical simulations. Four larger-to-smaller diameter ratios (D/d) of 4.0, 2.0, 1.43, and 1.19 are considered for the cylinder with a low mass ratio of 2. Numerical results reveal that D/d significantly influences vibration responses and the vortex shedding process. The case with D/d = 1.43 can effectively reduce vibration amplitudes. The wake vortices are shed in cellular patterns along the cylinder span, with a distinct frequency for each cell. A direct and “X-shaped” connection of wake vortex-shedding modes occurs between different vortex cells, and a loop connection appears between the same cell vortices. A new wake pattern entitled the “out-of-phase vortex shedding” is found downstream of the smaller cylinder at D/d = 2.0. This is manifested by the wake vortices not being shed at a fixed frequency and intensity. The essential reason for this phenomenon lies in a non-lock-in condition between the structural vibration and vortex shedding frequencies of the smaller cylinder. As D/d decreases, a coherence between vortex cells is enhanced, leading to a disappearance of the “out-of-phase vortex shedding.”

Categories: Latest papers in fluid mechanics

### Resolving the three-dimensional structure of particles that are aerodynamically clustered by a turbulent flow

Physics of Fluids, Volume 31, Issue 7, July 2019.

We report the first definitive experimental measurement of the four-dimensional (three spatial and one temporal) structure of particles that are aerodynamically clustered. High-speed tomographic imaging of a particle-laden turbulent flow was utilized to detect the temporal evolution of particle clusters at the exit of a long pipe. The measurements confirm that the particle clusters are coherent and ropelike in shape, rather than sheetlike, resolving a question that was not possible to address from previous two-dimensional measurements. These clusters are present right from the exit plane, where they are preferentially located near the jet edge, suggesting that they are generated inside the pipe close to the pipe wall.

We report the first definitive experimental measurement of the four-dimensional (three spatial and one temporal) structure of particles that are aerodynamically clustered. High-speed tomographic imaging of a particle-laden turbulent flow was utilized to detect the temporal evolution of particle clusters at the exit of a long pipe. The measurements confirm that the particle clusters are coherent and ropelike in shape, rather than sheetlike, resolving a question that was not possible to address from previous two-dimensional measurements. These clusters are present right from the exit plane, where they are preferentially located near the jet edge, suggesting that they are generated inside the pipe close to the pipe wall.

Categories: Latest papers in fluid mechanics

### Simulation of Io’s plumes and Jupiter’s plasma torus

Physics of Fluids, Volume 31, Issue 7, July 2019.

Io is a highly volcanic satellite of Jupiter. Its giant plumes rise hundreds of kilometers, creating large targets for incoming ions as Jupiter’s plasma torus overtakes Io in its orbit. Neutral material from Io’s sublimation atmosphere and volcanic plumes supplies the plasma torus, but the details of the interaction between neutral gas at Io and ions in the torus are not well understood. This paper suggests a process by which plume material is energized and ionized so as to supply the torus. We present three-dimensional direct simulation Monte Carlo simulations of giant plumes being bombarded by S+ and O+ ions which are moved based on precomputed electric and magnetic fields. The dependence of the plume/plasma interaction on the plume’s location on Io is investigated. The plume/plasma interaction is seen to be asymmetric even for a plume at the subplasma point because of the electric field that arises in an Io-fixed reference frame. Plasma is found to inflate and heat plume canopies and to give rise to a large, diffuse neutral cloud over the plume’s entire hemisphere. We also find that plasma can explain the thickness of red deposition rings observed on Io.

Io is a highly volcanic satellite of Jupiter. Its giant plumes rise hundreds of kilometers, creating large targets for incoming ions as Jupiter’s plasma torus overtakes Io in its orbit. Neutral material from Io’s sublimation atmosphere and volcanic plumes supplies the plasma torus, but the details of the interaction between neutral gas at Io and ions in the torus are not well understood. This paper suggests a process by which plume material is energized and ionized so as to supply the torus. We present three-dimensional direct simulation Monte Carlo simulations of giant plumes being bombarded by S+ and O+ ions which are moved based on precomputed electric and magnetic fields. The dependence of the plume/plasma interaction on the plume’s location on Io is investigated. The plume/plasma interaction is seen to be asymmetric even for a plume at the subplasma point because of the electric field that arises in an Io-fixed reference frame. Plasma is found to inflate and heat plume canopies and to give rise to a large, diffuse neutral cloud over the plume’s entire hemisphere. We also find that plasma can explain the thickness of red deposition rings observed on Io.

Categories: Latest papers in fluid mechanics

### Pressure drop reduction of power-law fluids in hydrophobic microgrooved channels

Physics of Fluids, Volume 31, Issue 7, July 2019.

Using hydrophobic surfaces is one of the efficient methods to preserve energy in fluid transfer systems. However, the studies have been concentrated on Newtonian fluids despite the wide applications of non-Newtonian fluids in daily life and many industries such as the biological, foodstuff, chemical, petroleum, cosmetic, and lab on a chip fields. In this study, we consider power-law fluids as a typical example of non-Newtonian fluids and investigate the effect of hydrophobic microgrooves on the pressure drop in channels by utilizing the phase field method. We demonstrate that the optimum size of the rectangular microgrooves in which the maximum pressure drop reduction (PDR) happens for both the considered Newtonian and non-Newtonian fluids is identical, but the PDR is different for the Newtonian and non-Newtonian fluids. For shear-thickening fluids, the PDR is more than shear-thinning fluids, which means that using the hydrophobic surfaces in dilatant fluids provides the best performance. It is seen that pressure drop reduces more at lower Reynolds numbers. We also investigate the efficiency of the microgrooved surfaces in convergent and divergent channels for both the Newtonian and non-Newtonian fluids and find the critical slope angles for a specific length of the channels in which the hydrophobic microgrooves have a sufficient performance in the PDR and stability.

Using hydrophobic surfaces is one of the efficient methods to preserve energy in fluid transfer systems. However, the studies have been concentrated on Newtonian fluids despite the wide applications of non-Newtonian fluids in daily life and many industries such as the biological, foodstuff, chemical, petroleum, cosmetic, and lab on a chip fields. In this study, we consider power-law fluids as a typical example of non-Newtonian fluids and investigate the effect of hydrophobic microgrooves on the pressure drop in channels by utilizing the phase field method. We demonstrate that the optimum size of the rectangular microgrooves in which the maximum pressure drop reduction (PDR) happens for both the considered Newtonian and non-Newtonian fluids is identical, but the PDR is different for the Newtonian and non-Newtonian fluids. For shear-thickening fluids, the PDR is more than shear-thinning fluids, which means that using the hydrophobic surfaces in dilatant fluids provides the best performance. It is seen that pressure drop reduces more at lower Reynolds numbers. We also investigate the efficiency of the microgrooved surfaces in convergent and divergent channels for both the Newtonian and non-Newtonian fluids and find the critical slope angles for a specific length of the channels in which the hydrophobic microgrooves have a sufficient performance in the PDR and stability.

Categories: Latest papers in fluid mechanics

### Aging continuous time random walks in fluids

Physics of Fluids, Volume 31, Issue 7, July 2019.

The subject of aging continuous time random walks (CTRWs) has attracted increasing attention in recent years. To describe the aging behaviors of random particles whose jumps are biased by a nonhomogeneous velocity field, we propose herein a generalized scheme of aging CTRWs in flows and obtain the corresponding generalized master equation in Fourier–Laplace space for probability density functions. Moreover, we derive the generalized aging advection diffusion equation for particles with a power law waiting time and Gaussian jump length densities, investigate the corresponding ensemble and time mean square displacements, and show how anomalous diffusion depends on the age of the process and on the moving fluids.

The subject of aging continuous time random walks (CTRWs) has attracted increasing attention in recent years. To describe the aging behaviors of random particles whose jumps are biased by a nonhomogeneous velocity field, we propose herein a generalized scheme of aging CTRWs in flows and obtain the corresponding generalized master equation in Fourier–Laplace space for probability density functions. Moreover, we derive the generalized aging advection diffusion equation for particles with a power law waiting time and Gaussian jump length densities, investigate the corresponding ensemble and time mean square displacements, and show how anomalous diffusion depends on the age of the process and on the moving fluids.

Categories: Latest papers in fluid mechanics

### Viscoelastic properties of suspensions of noncolloidal hard spheres in a molten polymer

Physics of Fluids, Volume 31, Issue 7, July 2019.

We report an experimental study on suspensions of solid particles in a viscoelastic polymer matrix. A commercial entangled poly([math]-caprolactone) was used as the suspending fluid. Noncolloidal solid spheres (diameter = 15 μm) made of polymethylmethacrylate were dispersed in the polymer via a solvent casting method. The volume fraction of the spheres was varied from 5% to 30%, thus allowing to explore both dilute and concentrated regimes. Electron scanning microscopy demonstrated homogeneous dispersion of the spheres in the matrix. We measured the rheological properties of the suspensions both in linear and nonlinear regimes with both dynamic and transient tests. The experimental results demonstrate the reinforcement effect of the particles. Both viscous and elastic moduli increase as the concentration of the particles is increased. The results show good agreement with available theories, simulations, and previous experimental data. In particular, the second order parameter of the quadratic equation that describes the dependence of the shear viscosity of the suspension upon the volume fraction of particles is in agreement with the predicted value found by Batchelor [G. K. Batchelor and J. T. Green, “The hydrodynamic interaction of two small freely-moving spheres in a linear flow field,” J. Fluid Mech. 56, 375–400 (1972); G. K. Batchelor and J. T. Green, “The determination of the bulk stress in a suspension of spherical particles to order c2,” J. Fluid Mech. 56, 401–427 (1972); and G. K. Batchelor, “The effect of Brownian motion on the bulk stress in a suspension of spherical particles,” J. Fluid Mech. 83, 97–117 (1977)]. We probe experimentally that the linear rheological behavior of suspensions of particles in viscoelastic fluids is the same as for Newtonian fluids.

We report an experimental study on suspensions of solid particles in a viscoelastic polymer matrix. A commercial entangled poly([math]-caprolactone) was used as the suspending fluid. Noncolloidal solid spheres (diameter = 15 μm) made of polymethylmethacrylate were dispersed in the polymer via a solvent casting method. The volume fraction of the spheres was varied from 5% to 30%, thus allowing to explore both dilute and concentrated regimes. Electron scanning microscopy demonstrated homogeneous dispersion of the spheres in the matrix. We measured the rheological properties of the suspensions both in linear and nonlinear regimes with both dynamic and transient tests. The experimental results demonstrate the reinforcement effect of the particles. Both viscous and elastic moduli increase as the concentration of the particles is increased. The results show good agreement with available theories, simulations, and previous experimental data. In particular, the second order parameter of the quadratic equation that describes the dependence of the shear viscosity of the suspension upon the volume fraction of particles is in agreement with the predicted value found by Batchelor [G. K. Batchelor and J. T. Green, “The hydrodynamic interaction of two small freely-moving spheres in a linear flow field,” J. Fluid Mech. 56, 375–400 (1972); G. K. Batchelor and J. T. Green, “The determination of the bulk stress in a suspension of spherical particles to order c2,” J. Fluid Mech. 56, 401–427 (1972); and G. K. Batchelor, “The effect of Brownian motion on the bulk stress in a suspension of spherical particles,” J. Fluid Mech. 83, 97–117 (1977)]. We probe experimentally that the linear rheological behavior of suspensions of particles in viscoelastic fluids is the same as for Newtonian fluids.

Categories: Latest papers in fluid mechanics

### Scaling and spatial intermittency of thermal dissipation in turbulent convection

Physics of Fluids, Volume 31, Issue 7, July 2019.

We derive scaling relations for the thermal dissipation rate in the bulk and in the boundary layers for moderate and large Prandtl number (Pr) convection. Using direct numerical simulations of Rayleigh-Bénard convection, we show that the thermal dissipation in the bulk is suppressed compared to passive scalar dissipation. The suppression is stronger for large Pr. We further show that the dissipation in the boundary layers dominates that in the bulk for both moderate and large Pr. The probability distribution functions of thermal dissipation rate, both in the bulk and in the boundary layers, are stretched exponential, similar to passive scalar dissipation.

We derive scaling relations for the thermal dissipation rate in the bulk and in the boundary layers for moderate and large Prandtl number (Pr) convection. Using direct numerical simulations of Rayleigh-Bénard convection, we show that the thermal dissipation in the bulk is suppressed compared to passive scalar dissipation. The suppression is stronger for large Pr. We further show that the dissipation in the boundary layers dominates that in the bulk for both moderate and large Pr. The probability distribution functions of thermal dissipation rate, both in the bulk and in the boundary layers, are stretched exponential, similar to passive scalar dissipation.

Categories: Latest papers in fluid mechanics

### The spontaneous breaking of axisymmetry in shallow rotating flows

Physics of Fluids, Volume 31, Issue 7, July 2019.

We show that the axial symmetry of a shallow rotating flow is spontaneously broken in the absence of an externally forced velocity gradient. It is caused by an instability excited by the gradients that arise from the axisymmetric counter-rotating vortices. The experimental setup consists of an electrolyte poured into a cylindrical container with radius R and height h and subject to electromagnetic forcing caused by an axial magnetic field and a radial current (J) leading to an azimuthal rotation Vθ. The flow motion is considered to be two-dimensional at large aspect ratio (R/h) and low Reynolds number, Re = Vθh/ν, where ν is the kinematic viscosity. At a moderate aspect ratio, we record the existence of an axisymmetric vortex at the edge caused by the no-slip boundary condition at the walls. When Re is increased by changing h or J, the flow becomes unstable at the radial position where gradients exist due to the edge vortices at a critical Reynolds number of about 220. The most unstable mode of this nonaxisymmetric instability is found to be m = 1 followed by m = 2 and other higher mode numbers. Using perturbation theory, we found that two counter-rotating vortices that are in azimuthal motion are unstable when subject to nonaxisymmetric perturbations with the onset of low azimuthal mode numbers in agreement with the experiment. We conclude that the axial symmetry breaking in shallow rotating flows occurs at relatively low Reynolds numbers caused by the gradients generated by the vortices in the height-radial plane.

We show that the axial symmetry of a shallow rotating flow is spontaneously broken in the absence of an externally forced velocity gradient. It is caused by an instability excited by the gradients that arise from the axisymmetric counter-rotating vortices. The experimental setup consists of an electrolyte poured into a cylindrical container with radius R and height h and subject to electromagnetic forcing caused by an axial magnetic field and a radial current (J) leading to an azimuthal rotation Vθ. The flow motion is considered to be two-dimensional at large aspect ratio (R/h) and low Reynolds number, Re = Vθh/ν, where ν is the kinematic viscosity. At a moderate aspect ratio, we record the existence of an axisymmetric vortex at the edge caused by the no-slip boundary condition at the walls. When Re is increased by changing h or J, the flow becomes unstable at the radial position where gradients exist due to the edge vortices at a critical Reynolds number of about 220. The most unstable mode of this nonaxisymmetric instability is found to be m = 1 followed by m = 2 and other higher mode numbers. Using perturbation theory, we found that two counter-rotating vortices that are in azimuthal motion are unstable when subject to nonaxisymmetric perturbations with the onset of low azimuthal mode numbers in agreement with the experiment. We conclude that the axial symmetry breaking in shallow rotating flows occurs at relatively low Reynolds numbers caused by the gradients generated by the vortices in the height-radial plane.

Categories: Latest papers in fluid mechanics

### Mechanism of pressure oscillation in Taylor-Couette-Poiseuille flow with abruptly contracting and expanding annular gap

Physics of Fluids, Volume 31, Issue 7, July 2019.

This study numerically investigates the effects of an abruptly contracting and expanding annular gap on the propagation of Taylor vortices in Taylor-Couette-Poiseuille flow. The results show that the pressure drop between the inlet and the outlet exhibits oscillations with low frequency and large amplitude. The nondimensional amplitude of oscillating pressure increases linearly with an increase in the rotating Reynolds number, whereas the nondimensional oscillating frequency remains nearly invariant with varying rotating and axial Reynolds numbers. Owing to the alternate action of counter-rotating Taylor vortex pairs in front of the block, local flow resistance periodically increases and decreases, resulting in the pressure drop oscillation. By analyzing the drift velocity and wavelength of the propagating Taylor vortex pair, a prediction model for the oscillating frequency is developed. Its results show that the nondimensional frequency is proportional to the blockage ratio. With an increase in the latter, the oscillating amplitude nonmonotonically changes as a result of the tunneling phenomenon, whereby the anticlockwise rotating Taylor roller is punctured by axial flow. Based on the above mechanism of pressure oscillation, the structure of a vortex breaker is proposed that can effectively reduce the oscillation in pressure.

This study numerically investigates the effects of an abruptly contracting and expanding annular gap on the propagation of Taylor vortices in Taylor-Couette-Poiseuille flow. The results show that the pressure drop between the inlet and the outlet exhibits oscillations with low frequency and large amplitude. The nondimensional amplitude of oscillating pressure increases linearly with an increase in the rotating Reynolds number, whereas the nondimensional oscillating frequency remains nearly invariant with varying rotating and axial Reynolds numbers. Owing to the alternate action of counter-rotating Taylor vortex pairs in front of the block, local flow resistance periodically increases and decreases, resulting in the pressure drop oscillation. By analyzing the drift velocity and wavelength of the propagating Taylor vortex pair, a prediction model for the oscillating frequency is developed. Its results show that the nondimensional frequency is proportional to the blockage ratio. With an increase in the latter, the oscillating amplitude nonmonotonically changes as a result of the tunneling phenomenon, whereby the anticlockwise rotating Taylor roller is punctured by axial flow. Based on the above mechanism of pressure oscillation, the structure of a vortex breaker is proposed that can effectively reduce the oscillation in pressure.

Categories: Latest papers in fluid mechanics

### Collision of a steepened wave with a blast wave in dusty real reacting gases

Physics of Fluids, Volume 31, Issue 7, July 2019.

In this paper, we study the collision of a one-dimensional steepened wave with a blast wave for the system of partial equations describing the unsteady flow of dusty real reacting gases with the same γ-law. The real gas is characterized by a van der Waals type equation of state. Special attention is devoted to analyzing the effects of real, reaction, and dusty gas parameters on the steepened wave. The amplitudes of the reflected and/or transmitted waves along with the jump in shock acceleration after the interaction are also obtained.

In this paper, we study the collision of a one-dimensional steepened wave with a blast wave for the system of partial equations describing the unsteady flow of dusty real reacting gases with the same γ-law. The real gas is characterized by a van der Waals type equation of state. Special attention is devoted to analyzing the effects of real, reaction, and dusty gas parameters on the steepened wave. The amplitudes of the reflected and/or transmitted waves along with the jump in shock acceleration after the interaction are also obtained.

Categories: Latest papers in fluid mechanics

### Effective mean free path and viscosity of confined gases

Physics of Fluids, Volume 31, Issue 7, July 2019.

The molecular mean free path (MFP) of gases in confined geometries is numerically evaluated by means of the direct simulation Monte Carlo method and molecular dynamics simulations. Our results show that if calculations take into account not only intermolecular interactions between gas molecules but also collisions between gas molecules and wall atoms, then a space-dependent MFP is obtained. The latter, in turn, permits one to define an effective viscosity of confined gases that also varies spatially. Both the gas MFP and viscosity variation in surface-confined systems have been questioned in the past. In this work, we demonstrate that this effective viscosity derived from our MFP calculations is consistent with those deduced from the linear-response relationship between the shear stress and strain rate using independent nonequilibrium Couette-style simulations as well as the equilibrium Green-Kubo predictions.

The molecular mean free path (MFP) of gases in confined geometries is numerically evaluated by means of the direct simulation Monte Carlo method and molecular dynamics simulations. Our results show that if calculations take into account not only intermolecular interactions between gas molecules but also collisions between gas molecules and wall atoms, then a space-dependent MFP is obtained. The latter, in turn, permits one to define an effective viscosity of confined gases that also varies spatially. Both the gas MFP and viscosity variation in surface-confined systems have been questioned in the past. In this work, we demonstrate that this effective viscosity derived from our MFP calculations is consistent with those deduced from the linear-response relationship between the shear stress and strain rate using independent nonequilibrium Couette-style simulations as well as the equilibrium Green-Kubo predictions.

Categories: Latest papers in fluid mechanics

### Development of specific structures occurring from hyper-breakable vorticity

Physics of Fluids, Volume 31, Issue 7, July 2019.

The spatial development of hyperbreakable vorticity in a supersonic coaxial flow with an annular swirl is investigated using direct numerical simulation at Mach number 1.5. The results show that the unstable modes originate from inside and outside the vortex depending on the ratio of vorticity thicknesses and then specific structures develop with small scales as distinct from conventional shear flows; furthermore, the evolutions lead to generate a number of fine scales due to the secondary instability. The mechanism is caused by the instability due to the helicity profile in addition to the barotropic instability based on the inflection point of the inner vorticity. This study strongly indicates that rapid evolutions on a plane perpendicular to the streamwise direction are insensitive to compressibility effects in supersonic flows. Therefore, the novel vorticity is found to undergo a breakdown at a short distance.

The spatial development of hyperbreakable vorticity in a supersonic coaxial flow with an annular swirl is investigated using direct numerical simulation at Mach number 1.5. The results show that the unstable modes originate from inside and outside the vortex depending on the ratio of vorticity thicknesses and then specific structures develop with small scales as distinct from conventional shear flows; furthermore, the evolutions lead to generate a number of fine scales due to the secondary instability. The mechanism is caused by the instability due to the helicity profile in addition to the barotropic instability based on the inflection point of the inner vorticity. This study strongly indicates that rapid evolutions on a plane perpendicular to the streamwise direction are insensitive to compressibility effects in supersonic flows. Therefore, the novel vorticity is found to undergo a breakdown at a short distance.

Categories: Latest papers in fluid mechanics

### Phenomenology of droplet collision hydrodynamics on wetting and non-wetting spheres

Physics of Fluids, Volume 31, Issue 7, July 2019.

In this study, the spreading characteristics of water droplets impacted on a solid spherical target have been investigated experimentally and theoretically. Droplet impact and postimpact feature studies have been conducted on hydrophilic and superhydrophobic spherical surfaces. Effects of the impact Weber number and target-to-drop diameter ratio on the spreading hydrodynamics have been discussed. Postcollision dynamics are explored with side and top views of impaction phenomenon using a high speed imaging technique. The morphological outcome of this impingement process has been quantitatively discussed with three geometric parameters, namely, liquid film thickness at the north-pole of the target surface, spread factor, and the maximum spread angle. Observations revel that spread factor and the maximum spread angle increases with the decrease in the size of the spherical target, whereas opposite of this is true for liquid film thickness at the north-pole of the target surface. Temporal variations of liquid film thickness at the north pole of the target have been plotted and found in agreement with the theoretical predictions made in the earlier studies. Finally, a mathematical model based on the energy balance principle has been proposed to predict the maximum spread angle on spherical targets. The theoretical values are found in good agreement with the experimental results for a wide range of spherical diameters studied. The findings may have implications toward a better understanding of fluid wetting, spraying, and coating behavior of complex shapes and geometries.

In this study, the spreading characteristics of water droplets impacted on a solid spherical target have been investigated experimentally and theoretically. Droplet impact and postimpact feature studies have been conducted on hydrophilic and superhydrophobic spherical surfaces. Effects of the impact Weber number and target-to-drop diameter ratio on the spreading hydrodynamics have been discussed. Postcollision dynamics are explored with side and top views of impaction phenomenon using a high speed imaging technique. The morphological outcome of this impingement process has been quantitatively discussed with three geometric parameters, namely, liquid film thickness at the north-pole of the target surface, spread factor, and the maximum spread angle. Observations revel that spread factor and the maximum spread angle increases with the decrease in the size of the spherical target, whereas opposite of this is true for liquid film thickness at the north-pole of the target surface. Temporal variations of liquid film thickness at the north pole of the target have been plotted and found in agreement with the theoretical predictions made in the earlier studies. Finally, a mathematical model based on the energy balance principle has been proposed to predict the maximum spread angle on spherical targets. The theoretical values are found in good agreement with the experimental results for a wide range of spherical diameters studied. The findings may have implications toward a better understanding of fluid wetting, spraying, and coating behavior of complex shapes and geometries.

Categories: Latest papers in fluid mechanics

### A study on dual role of viscosity on the stability of a viscous planar liquid sheet surrounded by inviscid gas streams of equal velocities, and prediction of resulting droplet distribution using maximum entropy formulation

Physics of Fluids, Volume 31, Issue 7, July 2019.

Low sensitivity to rheological properties of fluid and ability to produce fine sprays at low liquid pressure make airblast atomizers a preferred choice to process viscous liquids. Airblast atomizers essentially employ kinetic energy of coflowing gases to disintegrate a liquid sheet into fine spray. The present study employs the perturbation technique to carry out nonlinear investigation of the sinuous mode of instability in a thin planar viscous liquid sheet sandwiched between two inviscid gas streams moving at equal velocities. This paper analyzes temporal instability as well as droplet characteristics for a range of Reynolds numbers, Weber numbers, gas to liquid density ratios, and velocity ratios and reports the dual behavior of liquid viscosity at different operating conditions. For higher gas to liquid velocity ratios, this study identifies three regimes at all Weber numbers and gas to liquid density ratios: the first regime represents the stabilizing effect of viscosity at low Reynolds numbers, the second regime indicates the destabilizing effect of viscosity at intermediate Reynolds numbers, and the third regime further depicts the stabilizing effect of viscosity at high Reynolds numbers. However, for low gas to liquid velocity ratios, the third zone disappears at lower Weber numbers and gas to liquid density ratios, and the effect of viscosity is characterized by two regimes representing the weak stabilizing and destabilizing effect at low and relatively higher Reynolds numbers, respectively. Investigation of spray characteristics reveals that an increase in liquid viscosity produces relatively larger droplets at all flow conditions.

Low sensitivity to rheological properties of fluid and ability to produce fine sprays at low liquid pressure make airblast atomizers a preferred choice to process viscous liquids. Airblast atomizers essentially employ kinetic energy of coflowing gases to disintegrate a liquid sheet into fine spray. The present study employs the perturbation technique to carry out nonlinear investigation of the sinuous mode of instability in a thin planar viscous liquid sheet sandwiched between two inviscid gas streams moving at equal velocities. This paper analyzes temporal instability as well as droplet characteristics for a range of Reynolds numbers, Weber numbers, gas to liquid density ratios, and velocity ratios and reports the dual behavior of liquid viscosity at different operating conditions. For higher gas to liquid velocity ratios, this study identifies three regimes at all Weber numbers and gas to liquid density ratios: the first regime represents the stabilizing effect of viscosity at low Reynolds numbers, the second regime indicates the destabilizing effect of viscosity at intermediate Reynolds numbers, and the third regime further depicts the stabilizing effect of viscosity at high Reynolds numbers. However, for low gas to liquid velocity ratios, the third zone disappears at lower Weber numbers and gas to liquid density ratios, and the effect of viscosity is characterized by two regimes representing the weak stabilizing and destabilizing effect at low and relatively higher Reynolds numbers, respectively. Investigation of spray characteristics reveals that an increase in liquid viscosity produces relatively larger droplets at all flow conditions.

Categories: Latest papers in fluid mechanics

### Evaluation of particle-based continuum methods for a coupling with the direct simulation Monte Carlo method based on a nozzle expansion

Physics of Fluids, Volume 31, Issue 7, July 2019.

This paper investigates three different particle-based continuum methods, the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) and Fokker-Planck (ESFP) methods and the Low Diffusion (LD) method, for a coupling with the direct simulation Monte Carlo (DSMC) method. After a short description of the methods and their implementation, including the coupling concept for the LD-DSMC, simulation results of a nozzle expansion are compared with available experimental measurements and a DSMC simulation. Excellent agreement between ESBGK, ESFP, and DSMC can be observed in the throat of the nozzle, while the LD method fails to predict the correct velocity, temperature, and density profile. Further downstream, only the DSMC and the coupled ESBGK/ESFP-DSMC simulations are able to reproduce the measured rotational temperature profiles. A performance comparison shows the possible computational savings of a coupled ESBGK/ESFP-DSMC simulation, where a speedup of four orders of magnitude can be observed compared to a regular DSMC simulation.

This paper investigates three different particle-based continuum methods, the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) and Fokker-Planck (ESFP) methods and the Low Diffusion (LD) method, for a coupling with the direct simulation Monte Carlo (DSMC) method. After a short description of the methods and their implementation, including the coupling concept for the LD-DSMC, simulation results of a nozzle expansion are compared with available experimental measurements and a DSMC simulation. Excellent agreement between ESBGK, ESFP, and DSMC can be observed in the throat of the nozzle, while the LD method fails to predict the correct velocity, temperature, and density profile. Further downstream, only the DSMC and the coupled ESBGK/ESFP-DSMC simulations are able to reproduce the measured rotational temperature profiles. A performance comparison shows the possible computational savings of a coupled ESBGK/ESFP-DSMC simulation, where a speedup of four orders of magnitude can be observed compared to a regular DSMC simulation.

Categories: Latest papers in fluid mechanics