# Latest papers in fluid mechanics

### Direct molecular simulation of internal energy relaxation and dissociation in oxygen

Physics of Fluids, Volume DSMC2019, Issue 1, November 2019.

A variant of the direct simulation Monte Carlo (DSMC) method, referred to as direct molecular simulation (DMS), is used to study oxygen dissociation from first principles. The sole model input to the DMS calculations consists of 12 potential energy surfaces that govern O2 + O2 and O + O2 collisions, including all spin-spatial degenerate configurations, in the ground electronic state. DMS calculations are representative of the gas evolution behind a strong shock wave, where molecular oxygen excites rotationally and vibrationally before ultimately dissociating and reaching a quasi-steady-state (QSS). Vibrational relaxation time constants are presented for both O2 + O2 and O + O2 collisions and are found to agree closely with experimental data. Compared to O2 + O2 collisions, vibrational relaxation due to O + O2 collisions is found to be ten times faster and to have a weak dependence on temperature. Dissociation rate constants in the QSS dissociation phase are presented for both O2 + O2 and O + O2 collisions and agree (within experimental uncertainty) with rates inferred from shock-tube experiments. Both experiments and simulations indicate that the QSS dissociation rate coefficients for O + O2 interactions are about two times greater than the ones for O2 + O2. DMS calculations predict this to be a result of nonequilibrium (non-Boltzmann) internal energy distributions. Specifically, the increased dissociation rate is caused by faster vibrational relaxation, due to O + O2 collisions, which alters the vibrational energy distribution function in the QSS by populating higher energy states that readily dissociate. Although existing experimental data appear to support this prediction, experiments with lower uncertainty are needed for quantitative validation. The DMS data presented for rovibrational relaxation and dissociation in oxygen could be used to formulate models for DSMC and computational fluid dynamics methods.

A variant of the direct simulation Monte Carlo (DSMC) method, referred to as direct molecular simulation (DMS), is used to study oxygen dissociation from first principles. The sole model input to the DMS calculations consists of 12 potential energy surfaces that govern O2 + O2 and O + O2 collisions, including all spin-spatial degenerate configurations, in the ground electronic state. DMS calculations are representative of the gas evolution behind a strong shock wave, where molecular oxygen excites rotationally and vibrationally before ultimately dissociating and reaching a quasi-steady-state (QSS). Vibrational relaxation time constants are presented for both O2 + O2 and O + O2 collisions and are found to agree closely with experimental data. Compared to O2 + O2 collisions, vibrational relaxation due to O + O2 collisions is found to be ten times faster and to have a weak dependence on temperature. Dissociation rate constants in the QSS dissociation phase are presented for both O2 + O2 and O + O2 collisions and agree (within experimental uncertainty) with rates inferred from shock-tube experiments. Both experiments and simulations indicate that the QSS dissociation rate coefficients for O + O2 interactions are about two times greater than the ones for O2 + O2. DMS calculations predict this to be a result of nonequilibrium (non-Boltzmann) internal energy distributions. Specifically, the increased dissociation rate is caused by faster vibrational relaxation, due to O + O2 collisions, which alters the vibrational energy distribution function in the QSS by populating higher energy states that readily dissociate. Although existing experimental data appear to support this prediction, experiments with lower uncertainty are needed for quantitative validation. The DMS data presented for rovibrational relaxation and dissociation in oxygen could be used to formulate models for DSMC and computational fluid dynamics methods.

Categories: Latest papers in fluid mechanics

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

Physics of Fluids, Volume DSMC2019, Issue 1, November 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

### Direct simulation Monte Carlo on petaflop supercomputers and beyond

Physics of Fluids, Volume DSMC2019, Issue 1, November 2019.

The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief barrier to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method’s inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird’s 1994 formulation. Here, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We give a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.

The gold-standard definition of the Direct Simulation Monte Carlo (DSMC) method is given in the 1994 book by Bird [Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994)], which refined his pioneering earlier papers in which he first formulated the method. In the intervening 25 years, DSMC has become the method of choice for modeling rarefied gas dynamics in a variety of scenarios. The chief barrier to applying DSMC to more dense or even continuum flows is its computational expense compared to continuum computational fluid dynamics methods. The dramatic (nearly billion-fold) increase in speed of the largest supercomputers over the last 30 years has thus been a key enabling factor in using DSMC to model a richer variety of flows, due to the method’s inherent parallelism. We have developed the open-source SPARTA DSMC code with the goal of running DSMC efficiently on the largest machines, both current and future. It is largely an implementation of Bird’s 1994 formulation. Here, we describe algorithms used in SPARTA to enable DSMC to operate in parallel at the scale of many billions of particles or grid cells, or with billions of surface elements. We give a few examples of the kinds of fundamental physics questions and engineering applications that DSMC can address at these scales.

Categories: Latest papers in fluid mechanics

### On the Noble-Abel stiffened-gas equation of state

Physics of Fluids, Volume 31, Issue 11, November 2019.

The inviscid hydrodynamics of inert compressible media governed by the Euler equations of motion only require knowledge of a caloric equation of state e(p, [math]) for the material relating the internal energy e to the fluid pressure p and specific volume [math] (or density). For departures from the ideal gas behavior, simple equations of state such as the stiffened gas, Noble-Abel, or a hybrid recently generalized by Le Métayer and Saurel [“The Noble-Abel stiffened-gas equation of state,” Phys. Fluids 28, 046102 (2016)] can correctly model compressible flows in gases, liquids, and solids. However, reactive and multicomponent descriptions require a formal definition of temperature. In the present note, we formulate a general thermodynamically based method to determine the thermal equation of state T(p, [math]) compatible with a generic e(p, [math]) relation. We apply our method to the Noble-Abel Stiffened Gas equation of state and recover the closed form solution of Le Métayer and Saurel. We also show that variations of the model taking its exponent different from the ratio of specific heats do not permit to define a thermodynamic temperature.

The inviscid hydrodynamics of inert compressible media governed by the Euler equations of motion only require knowledge of a caloric equation of state e(p, [math]) for the material relating the internal energy e to the fluid pressure p and specific volume [math] (or density). For departures from the ideal gas behavior, simple equations of state such as the stiffened gas, Noble-Abel, or a hybrid recently generalized by Le Métayer and Saurel [“The Noble-Abel stiffened-gas equation of state,” Phys. Fluids 28, 046102 (2016)] can correctly model compressible flows in gases, liquids, and solids. However, reactive and multicomponent descriptions require a formal definition of temperature. In the present note, we formulate a general thermodynamically based method to determine the thermal equation of state T(p, [math]) compatible with a generic e(p, [math]) relation. We apply our method to the Noble-Abel Stiffened Gas equation of state and recover the closed form solution of Le Métayer and Saurel. We also show that variations of the model taking its exponent different from the ratio of specific heats do not permit to define a thermodynamic temperature.

Categories: Latest papers in fluid mechanics

### Wake transitions of flexible foils in a viscous uniform flow

Physics of Fluids, Volume 31, Issue 11, November 2019.

The effects of flexibility on the wake structures of a foil under a heaving motion in a viscous uniform flow are numerically studied using an immersed boundary method. An inspection of the phase diagram of the wake structures in a map of the chord-length-based dimensionless heaving amplitude (AL) and Strouhal number (StL) shows that the wake transition boundaries of the rigid foil are well predicted by constant amplitude-based Strouhal number (StA) lines, similar to previous studies. However, the wake transition boundaries of the flexible foil are predictable by constant StA lines only for high StL cases. A large deformation angle of a flexible foil by the amplitude difference and phase difference between the leading and trailing edge cross-stream displacements reduces the effective leading edge velocity, with an accompanying decrease in the leading edge circulation. However, the trailing edge circulation for a flexible foil is increased due to increased trailing edge amplitude. The sum of the leading and trailing edge circulations plays an important role in determining the wake pattern behind a rigid and flexible foil, and wake transitions are observed beyond critical circulations. The decrease in the thrust coefficient for large values of StL and AL is closely associated with the generation of a complex wake pattern behind a foil, and the complex wake is a direct consequence of sufficiently large leading edge circulation. A critical effective phase velocity in a vortex dipole model is proposed to predict the maximum thrust coefficient without a complex wake pattern.

The effects of flexibility on the wake structures of a foil under a heaving motion in a viscous uniform flow are numerically studied using an immersed boundary method. An inspection of the phase diagram of the wake structures in a map of the chord-length-based dimensionless heaving amplitude (AL) and Strouhal number (StL) shows that the wake transition boundaries of the rigid foil are well predicted by constant amplitude-based Strouhal number (StA) lines, similar to previous studies. However, the wake transition boundaries of the flexible foil are predictable by constant StA lines only for high StL cases. A large deformation angle of a flexible foil by the amplitude difference and phase difference between the leading and trailing edge cross-stream displacements reduces the effective leading edge velocity, with an accompanying decrease in the leading edge circulation. However, the trailing edge circulation for a flexible foil is increased due to increased trailing edge amplitude. The sum of the leading and trailing edge circulations plays an important role in determining the wake pattern behind a rigid and flexible foil, and wake transitions are observed beyond critical circulations. The decrease in the thrust coefficient for large values of StL and AL is closely associated with the generation of a complex wake pattern behind a foil, and the complex wake is a direct consequence of sufficiently large leading edge circulation. A critical effective phase velocity in a vortex dipole model is proposed to predict the maximum thrust coefficient without a complex wake pattern.

Categories: Latest papers in fluid mechanics

### Two-dimensional sub-aerial, submerged, and transitional granular slides

Physics of Fluids, Volume 31, Issue 11, November 2019.

The slide of granular material in nature and engineering can happen under air (subaerial), under a liquidlike water (submerged), or a transition between these two regimes, where a subaerial slide enters a liquid and becomes submerged. Here, we experimentally investigate these three slide regimes (i.e., subaerial, submerged, and transitional) in two dimensions, for various slope angles, material types, and bed roughness. The goal is to shed light on the complex morphodynamics and flow structure of these granular flows and also to provide comprehensive benchmarks for the validation and parametrization of the numerical models. The slide regime is found to be a major controller of the granular morphodynamics (e.g., shape evolution and internal flow structure). The time history of the runout distance for the subaerial and submerged cases present a similar three-phase trend (with acceleration, steady flow, and deceleration phases) tough with different spatiotemporal scales. Compared to the subaerial cases, the submerged cases show longer runout time and shorter final runout distances. The transitional trends, however, show additional deceleration and reacceleration. The observations suggest that the impact of slide angle, material type, and bed roughness on the morphodynamics is less significant where the material interacts with water. Flow structure, extracted using a granular particle image velocimetry technique, shows a relatively power-law velocity profile for the subaerial condition and strong circulations for the submerged condition. An unsteady theoretical model based on the µ(I) rheology is developed and is shown to be effective in the prediction of the average velocity of the granular mass.

The slide of granular material in nature and engineering can happen under air (subaerial), under a liquidlike water (submerged), or a transition between these two regimes, where a subaerial slide enters a liquid and becomes submerged. Here, we experimentally investigate these three slide regimes (i.e., subaerial, submerged, and transitional) in two dimensions, for various slope angles, material types, and bed roughness. The goal is to shed light on the complex morphodynamics and flow structure of these granular flows and also to provide comprehensive benchmarks for the validation and parametrization of the numerical models. The slide regime is found to be a major controller of the granular morphodynamics (e.g., shape evolution and internal flow structure). The time history of the runout distance for the subaerial and submerged cases present a similar three-phase trend (with acceleration, steady flow, and deceleration phases) tough with different spatiotemporal scales. Compared to the subaerial cases, the submerged cases show longer runout time and shorter final runout distances. The transitional trends, however, show additional deceleration and reacceleration. The observations suggest that the impact of slide angle, material type, and bed roughness on the morphodynamics is less significant where the material interacts with water. Flow structure, extracted using a granular particle image velocimetry technique, shows a relatively power-law velocity profile for the subaerial condition and strong circulations for the submerged condition. An unsteady theoretical model based on the µ(I) rheology is developed and is shown to be effective in the prediction of the average velocity of the granular mass.

Categories: Latest papers in fluid mechanics

### A modern perspective on flow instability and shockwave phenomena in reacting gas multiphase system excited by direct current

Physics of Fluids, Volume 31, Issue 11, November 2019.

A critical analysis of physical insights into ionization waves, plasma states, and attendant phenomena in a gas discharge plasma excited by direct current discussed in the literature is performed. A comparison between synergy bifurcation and kinetic bunching models shows that the former is undoubtedly close-to-perfect and “useful,” and it “is an accurate representation of the real world from the perspective of the intended uses of the model” in the range of gas pressures from 1 to 100 Torr, whereas the latter is obviously imperfect. The latter model is no perspective. The basic factors and ideas definitely established at the early stage of studying striations and current jumps in the discharge are briefly reviewed. The synergy aspect invoking the diffusion-reaction equations, catastrophe theory, and ionization equilibrium principle is demonstrated to permit us to better understand the physics of ionization waves and the underlying physical processes and also to establish a natural and useful link between the parameters of a physical system. Conditions and specific features of their formation and propagation directions are determined. Based on modern concepts of the physical nature of striations and current jumps, it is demonstrated that these ionization waves propagating in a gas discharge are typical ionization-diffusion shock waves.

A critical analysis of physical insights into ionization waves, plasma states, and attendant phenomena in a gas discharge plasma excited by direct current discussed in the literature is performed. A comparison between synergy bifurcation and kinetic bunching models shows that the former is undoubtedly close-to-perfect and “useful,” and it “is an accurate representation of the real world from the perspective of the intended uses of the model” in the range of gas pressures from 1 to 100 Torr, whereas the latter is obviously imperfect. The latter model is no perspective. The basic factors and ideas definitely established at the early stage of studying striations and current jumps in the discharge are briefly reviewed. The synergy aspect invoking the diffusion-reaction equations, catastrophe theory, and ionization equilibrium principle is demonstrated to permit us to better understand the physics of ionization waves and the underlying physical processes and also to establish a natural and useful link between the parameters of a physical system. Conditions and specific features of their formation and propagation directions are determined. Based on modern concepts of the physical nature of striations and current jumps, it is demonstrated that these ionization waves propagating in a gas discharge are typical ionization-diffusion shock waves.

Categories: Latest papers in fluid mechanics

### Analysis of the performance of a new developed shear stress transport model in a turbulent impinging jet flow

Physics of Fluids, Volume 31, Issue 11, November 2019.

In this work, a developed Shear Stress Transport (SST) model has been used for numerically simulating the problem of turbulent round jet impingement heat transfer. Based on the cross-diffusion correction activated in the logarithmic and wake parts of a region by using a blending function in the destruction term of turbulent kinetic energy k, the developed SST model is capable of recovering the effect of the pressure gradient ignored by the standard SST model. Also, the Kato-Launder model is added in the production term of k to consider the stagnating flows. The developed model has been investigated for turbulent round jets with the nozzle-plate spacing of 2, 4, and 6. The model is verified by comparing with the measurements and the results of the standard SST model, the SST with low-Re model, the Launder and Sharma model with the Yap model, the k-ω model, and the Reynolds-averaged Navier-Stokes/large eddy simulation model. Comparing with other referred methods, the developed model obtains accurate prediction in terms of velocity and pressure. As for heat transfer, it also possesses appropriate performance. Moreover, the developed model is sensitive to the pressure gradient, which helps the model be capable of reproducing accurate flow structures. By using the present model, it has been found that the velocity profiles are dominated by the turbulent kinetic energy away from walls. Meanwhile, the results show that the inner peak of heat transfer is connected with the radial pressure gradient at the stagnation point.

In this work, a developed Shear Stress Transport (SST) model has been used for numerically simulating the problem of turbulent round jet impingement heat transfer. Based on the cross-diffusion correction activated in the logarithmic and wake parts of a region by using a blending function in the destruction term of turbulent kinetic energy k, the developed SST model is capable of recovering the effect of the pressure gradient ignored by the standard SST model. Also, the Kato-Launder model is added in the production term of k to consider the stagnating flows. The developed model has been investigated for turbulent round jets with the nozzle-plate spacing of 2, 4, and 6. The model is verified by comparing with the measurements and the results of the standard SST model, the SST with low-Re model, the Launder and Sharma model with the Yap model, the k-ω model, and the Reynolds-averaged Navier-Stokes/large eddy simulation model. Comparing with other referred methods, the developed model obtains accurate prediction in terms of velocity and pressure. As for heat transfer, it also possesses appropriate performance. Moreover, the developed model is sensitive to the pressure gradient, which helps the model be capable of reproducing accurate flow structures. By using the present model, it has been found that the velocity profiles are dominated by the turbulent kinetic energy away from walls. Meanwhile, the results show that the inner peak of heat transfer is connected with the radial pressure gradient at the stagnation point.

Categories: Latest papers in fluid mechanics

### Advanced simulations of turbulent boundary layers under pressure-gradient conditions

Physics of Fluids, Volume 31, Issue 11, November 2019.

A high-Reynolds-number turbulent boundary layer experiencing pressure gradients is simulated with Reynolds-averaged Navier-Stokes (RANS) and hybrid RANS/LES (Large Eddy Simulation) advanced turbulence modeling approaches, namely, two eddy viscosity models, two Reynolds Stress models (RSMs), and Zonal Detached Eddy Simulation (ZDES) mode 3 which corresponds to a wall-modeled LES approach. Such a study is the first of its kind to the authors’ best knowledge. The test-case considered is the experimental work of Cuvier et al. [“Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology,” J. Turbul. 18, 929–972 (2017)]. Some modifications of the top wall geometry have been proposed to take into account the blockage effect of the boundary layers developing over the wind tunnel side walls so that statistically two-dimensional simulations are possible. Comparisons have shown that there are some difficulties in properly predicting the mean skin friction and the Reynolds stresses in the adverse-pressure-gradient region for the ZDES and RSMs. The mean velocity profiles in this region are, however, poorly reproduced by all models. The atypical profiles experimentally observed at the beginning of the favorable-pressure-gradient region are well reproduced by RSMs, one eddy viscosity model, and ZDES for the mean velocity; however, only ZDES is able to satisfactorily predict the Reynolds stresses at this station. A spectral analysis of streamwise velocity fluctuations and Reynolds shear stress by means of ZDES has allowed us to identify external energetic turbulent structures at y ≈ 0.5δ and of size λx ≈ 3δ which are probably responsible for these atypical profiles. The present numerical test-case may constitute a development base for turbulence modeling under pressure gradient effects.

A high-Reynolds-number turbulent boundary layer experiencing pressure gradients is simulated with Reynolds-averaged Navier-Stokes (RANS) and hybrid RANS/LES (Large Eddy Simulation) advanced turbulence modeling approaches, namely, two eddy viscosity models, two Reynolds Stress models (RSMs), and Zonal Detached Eddy Simulation (ZDES) mode 3 which corresponds to a wall-modeled LES approach. Such a study is the first of its kind to the authors’ best knowledge. The test-case considered is the experimental work of Cuvier et al. [“Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology,” J. Turbul. 18, 929–972 (2017)]. Some modifications of the top wall geometry have been proposed to take into account the blockage effect of the boundary layers developing over the wind tunnel side walls so that statistically two-dimensional simulations are possible. Comparisons have shown that there are some difficulties in properly predicting the mean skin friction and the Reynolds stresses in the adverse-pressure-gradient region for the ZDES and RSMs. The mean velocity profiles in this region are, however, poorly reproduced by all models. The atypical profiles experimentally observed at the beginning of the favorable-pressure-gradient region are well reproduced by RSMs, one eddy viscosity model, and ZDES for the mean velocity; however, only ZDES is able to satisfactorily predict the Reynolds stresses at this station. A spectral analysis of streamwise velocity fluctuations and Reynolds shear stress by means of ZDES has allowed us to identify external energetic turbulent structures at y ≈ 0.5δ and of size λx ≈ 3δ which are probably responsible for these atypical profiles. The present numerical test-case may constitute a development base for turbulence modeling under pressure gradient effects.

Categories: Latest papers in fluid mechanics

### Statistics of coherent structures in two-dimensional turbulent Rayleigh-Bénard convection

Physics of Fluids, Volume 31, Issue 11, November 2019.

Characterization of coherent structures in turbulent Rayleigh-Bénard convection using statistical measures is presented in the present work. Numerical simulations are carried out in a two-dimensional (2D) rectangular cell with aspect ratio 2 using air as the working fluid across four decades of Rayleigh number. The absence of one lateral dimension leads to entrapment of plumes which are consequently emitted in the form of thermal jets. Axial nonuniformity in thermal boundary layers is eliminated at high Rayleigh numbers. The so-called slope and 99% methods produce identical boundary layer thicknesses whose power law variation confirms theoretical inverse-Nu scaling. Turbulent kinetic energy budget unveils a transport-dissipation balance near the walls with buoyancy production nearly sustaining turbulent fluctuations in the bulk region. A higher threshold for the correlation between the vertical velocity and temperature results in faster convergence of plume and background share of dissipation, while decay in the volume fraction of the plume region continues. Exponential distribution of temperature fluctuations suggests the presence of hard turbulence at very large Rayleigh numbers with wider tails recording extreme fluctuating events. Changes in plume emission and its subsequent motion not only influence boundary layer instabilities but also cause departure from the −5/3 law in the frequency spectra.

Characterization of coherent structures in turbulent Rayleigh-Bénard convection using statistical measures is presented in the present work. Numerical simulations are carried out in a two-dimensional (2D) rectangular cell with aspect ratio 2 using air as the working fluid across four decades of Rayleigh number. The absence of one lateral dimension leads to entrapment of plumes which are consequently emitted in the form of thermal jets. Axial nonuniformity in thermal boundary layers is eliminated at high Rayleigh numbers. The so-called slope and 99% methods produce identical boundary layer thicknesses whose power law variation confirms theoretical inverse-Nu scaling. Turbulent kinetic energy budget unveils a transport-dissipation balance near the walls with buoyancy production nearly sustaining turbulent fluctuations in the bulk region. A higher threshold for the correlation between the vertical velocity and temperature results in faster convergence of plume and background share of dissipation, while decay in the volume fraction of the plume region continues. Exponential distribution of temperature fluctuations suggests the presence of hard turbulence at very large Rayleigh numbers with wider tails recording extreme fluctuating events. Changes in plume emission and its subsequent motion not only influence boundary layer instabilities but also cause departure from the −5/3 law in the frequency spectra.

Categories: Latest papers in fluid mechanics

### Effects of stroke deviation on hovering aerodynamic performance of flapping wings

Physics of Fluids, Volume 31, Issue 11, November 2019.

In this paper, the typical normal-hovering mode with different surging motions is numerically simulated by solving two-dimensional unsteady Navier-Stokes equations with the aim of investigating the effects of stroke deviation on aerodynamic performance. An elliptic wing model with 2% thickness is employed, conducting a horizontal motion (plunge), a vertical motion (surge), and a rotating motion (pitch). A low Reynolds number of 100 is adopted. The various surging motion in each half-stroke is defined by a half-sine or full-sine waveform, while the pitching and plunging motions are fixed for 16 patterns. The details of the aerodynamic force histories, vortex dynamics, induced jet effects, and time-averaged aerodynamics are systematically analyzed. The results show that for most patterns, stroke deviation plays a negative role in reducing lift and increasing energy consumption, which results in a decline of lifting efficiency. The forward surging motion that commences up the horizontal stroke plane attenuates the wake capture mechanism and reinforces the delayed stall mechanism. Compared to the typical normal-hovering pattern with no deviation, the resulting lift in pattern E decreases at the beginning of stroke and increases at the midstroke. The downward surging motion shows an opposite effect on the aerodynamics. The minimum power (−10.2%) is consumed in pattern F, although the minimum lift is generated in the meantime. In addition, the maximum lift augmentation of 8.7% is produced in pattern I along with the characteristic of power economy. Our study can provide advice on utilizing stroke deviation to increasing lift production and decreasing power consumption.

In this paper, the typical normal-hovering mode with different surging motions is numerically simulated by solving two-dimensional unsteady Navier-Stokes equations with the aim of investigating the effects of stroke deviation on aerodynamic performance. An elliptic wing model with 2% thickness is employed, conducting a horizontal motion (plunge), a vertical motion (surge), and a rotating motion (pitch). A low Reynolds number of 100 is adopted. The various surging motion in each half-stroke is defined by a half-sine or full-sine waveform, while the pitching and plunging motions are fixed for 16 patterns. The details of the aerodynamic force histories, vortex dynamics, induced jet effects, and time-averaged aerodynamics are systematically analyzed. The results show that for most patterns, stroke deviation plays a negative role in reducing lift and increasing energy consumption, which results in a decline of lifting efficiency. The forward surging motion that commences up the horizontal stroke plane attenuates the wake capture mechanism and reinforces the delayed stall mechanism. Compared to the typical normal-hovering pattern with no deviation, the resulting lift in pattern E decreases at the beginning of stroke and increases at the midstroke. The downward surging motion shows an opposite effect on the aerodynamics. The minimum power (−10.2%) is consumed in pattern F, although the minimum lift is generated in the meantime. In addition, the maximum lift augmentation of 8.7% is produced in pattern I along with the characteristic of power economy. Our study can provide advice on utilizing stroke deviation to increasing lift production and decreasing power consumption.

Categories: Latest papers in fluid mechanics

### Ultrasonic spinning rheometry test on the rheology of gelled food for making better tasting desserts

Physics of Fluids, Volume 31, Issue 11, November 2019.

Rheological properties of gelled foods that may relate to the physics of the fluids in the swallowing process of complex food components are determined by ultrasonic spinning rheometry (USR) [T. Yoshida et al., “Efficacy assessments in ultrasonic spinning rheometry: Linear viscoelastic analysis on non-Newtonian fluids,” J. Rheol. 63, 503–517 (2019)]. Through rheological evaluations of thixotropic gelled food, the inaccuracies in standard rheometer data to capture the true-rheological property are discussed first with steady rotational and oscillatory tests; the inaccuracies arise from commonly existing problems that cannot be directly observed in standard rheometers (wall-slip, shear banding, shear localization, elastic instability, etc.). The results evaluated by standard rheometers would be related to the measurements being specific response, depending on the geometry of the measurement device. The USR test discussed here shows the potential to overcome these problems in the rheological evaluation of gelled foods and reflects the advantages offered by USR such as spatial, local, and oscillation cycle measurements; the results with the transient flow curve that has not previously been discussed can be usefully interpreted, and the stability of the food materials in the unsteady shear displayed is of great importance in understanding which rheology indicates the better texture.

Rheological properties of gelled foods that may relate to the physics of the fluids in the swallowing process of complex food components are determined by ultrasonic spinning rheometry (USR) [T. Yoshida et al., “Efficacy assessments in ultrasonic spinning rheometry: Linear viscoelastic analysis on non-Newtonian fluids,” J. Rheol. 63, 503–517 (2019)]. Through rheological evaluations of thixotropic gelled food, the inaccuracies in standard rheometer data to capture the true-rheological property are discussed first with steady rotational and oscillatory tests; the inaccuracies arise from commonly existing problems that cannot be directly observed in standard rheometers (wall-slip, shear banding, shear localization, elastic instability, etc.). The results evaluated by standard rheometers would be related to the measurements being specific response, depending on the geometry of the measurement device. The USR test discussed here shows the potential to overcome these problems in the rheological evaluation of gelled foods and reflects the advantages offered by USR such as spatial, local, and oscillation cycle measurements; the results with the transient flow curve that has not previously been discussed can be usefully interpreted, and the stability of the food materials in the unsteady shear displayed is of great importance in understanding which rheology indicates the better texture.

Categories: Latest papers in fluid mechanics

### Velocity of a large bubble rising in a stagnant liquid inside an inclined rectangular channel

Physics of Fluids, Volume 31, Issue 11, November 2019.

The velocity of large air bubbles rising in an inclined rectangular channel filled up with stagnant water is investigated within the inertial flow regime. The experiments based on bubble observation by means of a high-speed camera are carried-out in a versatile channel with easily adaptable geometry over a wide range of inclination angles. The results obtained in vertical channels of various aspect ratios are confronted with the previous analytical predictions to confirm bubble velocity scaling based on the channel perimeter. The extrapolation of velocity measurements done at very low inclinations then provides the translation velocities of large bubbles corresponding to horizontal channel placements. These velocities agree well with the results of previous channel emptying experiments and suggest velocity scaling based on the channel height. Markedly different dependences of the bubble rise velocity on the channel inclination are observed in flat and tall channels. The analysis of our experimental data provides a simple model for the prediction of the bubble rise velocity in inclined rectangular channels. The effects of leveling and buoyancy, which are jointly acting on bubbles in inclined channels, are incorporated into the model through two principal parameters: the limiting bubble velocities achieved at the horizontal and vertical channel placement. Considering the inertial regime of large Taylor bubbles, these limiting velocities are predictable with a sufficient accuracy.

The velocity of large air bubbles rising in an inclined rectangular channel filled up with stagnant water is investigated within the inertial flow regime. The experiments based on bubble observation by means of a high-speed camera are carried-out in a versatile channel with easily adaptable geometry over a wide range of inclination angles. The results obtained in vertical channels of various aspect ratios are confronted with the previous analytical predictions to confirm bubble velocity scaling based on the channel perimeter. The extrapolation of velocity measurements done at very low inclinations then provides the translation velocities of large bubbles corresponding to horizontal channel placements. These velocities agree well with the results of previous channel emptying experiments and suggest velocity scaling based on the channel height. Markedly different dependences of the bubble rise velocity on the channel inclination are observed in flat and tall channels. The analysis of our experimental data provides a simple model for the prediction of the bubble rise velocity in inclined rectangular channels. The effects of leveling and buoyancy, which are jointly acting on bubbles in inclined channels, are incorporated into the model through two principal parameters: the limiting bubble velocities achieved at the horizontal and vertical channel placement. Considering the inertial regime of large Taylor bubbles, these limiting velocities are predictable with a sufficient accuracy.

Categories: Latest papers in fluid mechanics

### Two-phase flow simulation of scour beneath a vibrating pipeline during the tunnel erosion stage

Physics of Fluids, Volume 31, Issue 11, November 2019.

A new numerical model is developed to simulate and investigate scour beneath a vibrating pipe during the tunnel erosion stage. This study is motivated by the fact that existing numerical models are not able to properly simulate scour under a vibrating pipeline, and the underlying physical mechanisms are not well understood due to the complex fluid-structure-sediment interaction. The present model incorporates the hybrid fictitious domain-immersed boundary method into a recently developed rheology-based two-phase model. The present model is validated against published experiment results of flow beneath a vibrating pipeline near a rigid boundary and scour beneath a fixed pipe. The flow velocity at the gap and the scour profile beneath the pipe are generally well produced by the model. Subsequently, the proposed model is applied to simulate scour under a vibrating pipe with different vibration amplitudes and frequencies. Among other things, it is found that maximum pipe acceleration has a dominant effect on the underlying physics that induce scour, irrespective of the combination of the vibration amplitude and frequency. An explanation for this finding is proposed based on various quantitative simulated results.

A new numerical model is developed to simulate and investigate scour beneath a vibrating pipe during the tunnel erosion stage. This study is motivated by the fact that existing numerical models are not able to properly simulate scour under a vibrating pipeline, and the underlying physical mechanisms are not well understood due to the complex fluid-structure-sediment interaction. The present model incorporates the hybrid fictitious domain-immersed boundary method into a recently developed rheology-based two-phase model. The present model is validated against published experiment results of flow beneath a vibrating pipeline near a rigid boundary and scour beneath a fixed pipe. The flow velocity at the gap and the scour profile beneath the pipe are generally well produced by the model. Subsequently, the proposed model is applied to simulate scour under a vibrating pipe with different vibration amplitudes and frequencies. Among other things, it is found that maximum pipe acceleration has a dominant effect on the underlying physics that induce scour, irrespective of the combination of the vibration amplitude and frequency. An explanation for this finding is proposed based on various quantitative simulated results.

Categories: Latest papers in fluid mechanics

### Publisher’s Note: “A unified analysis of nano-to-microscale particle dispersion in tubular blood flow” [Phys. Fluids 31, 081903 (2019)]

Physics of Fluids, Volume 31, Issue 11, November 2019.

Categories: Latest papers in fluid mechanics