# Latest papers in fluid mechanics

### Phase-space dynamics of near-wall streaks in wall-bounded turbulence with spanwise oscillation

Physics of Fluids, Volume 31, Issue 12, December 2019.

This work presents systematical investigations on the skin-friction drag reduction (DR) of turbulent channel flow subjected to spanwise wall oscillation using direct numerical simulation. Altogether 12 different oscillatory cases have been studied with a reference at Reτ = 200, varying the controlling parameters characterized by maximum wall velocity Wm+ and oscillation period T+. Some of the previously established facts have been reproduced by our analysis with a new focus on the phase-space dynamics of the near-wall streaks, on the basis of statistical data over entire oscillation periods and over phasewise variations. It is revealed that streamwise vortices are generated in the vicinity of oscillation walls, disrupting the formation of near-wall low-speed streaks. Although the overall turbulence is weakened, the Stokes layer is thicker within wall acceleration phases for larger Wm+, which causes the turbulence intensity to increase in the upper viscous sublayer. In addition, regarding the effect of T+, a long oscillation period promotes the formation of energetic near-wall structures, while for short T+, the streak-generation time scale preferentially restricts the growth of spanwise streaks. From a new vorticity-transport perspective of the Reynolds shear stress, our results further indicate that high drag-reducing phenomena are connected to the near-wall sweep events, and the shear stress variation is principally driven by the distortion of the spanwise transport of wall-normal vorticity, i.e., vortex tilting/stretching. The DR process is seen to be linked to the increase in enstrophy and turbulence-energy dissipation in the near-wall region.

This work presents systematical investigations on the skin-friction drag reduction (DR) of turbulent channel flow subjected to spanwise wall oscillation using direct numerical simulation. Altogether 12 different oscillatory cases have been studied with a reference at Reτ = 200, varying the controlling parameters characterized by maximum wall velocity Wm+ and oscillation period T+. Some of the previously established facts have been reproduced by our analysis with a new focus on the phase-space dynamics of the near-wall streaks, on the basis of statistical data over entire oscillation periods and over phasewise variations. It is revealed that streamwise vortices are generated in the vicinity of oscillation walls, disrupting the formation of near-wall low-speed streaks. Although the overall turbulence is weakened, the Stokes layer is thicker within wall acceleration phases for larger Wm+, which causes the turbulence intensity to increase in the upper viscous sublayer. In addition, regarding the effect of T+, a long oscillation period promotes the formation of energetic near-wall structures, while for short T+, the streak-generation time scale preferentially restricts the growth of spanwise streaks. From a new vorticity-transport perspective of the Reynolds shear stress, our results further indicate that high drag-reducing phenomena are connected to the near-wall sweep events, and the shear stress variation is principally driven by the distortion of the spanwise transport of wall-normal vorticity, i.e., vortex tilting/stretching. The DR process is seen to be linked to the increase in enstrophy and turbulence-energy dissipation in the near-wall region.

Categories: Latest papers in fluid mechanics

### Scales of turbulence in open-channel flows with low relative submergence

Physics of Fluids, Volume 31, Issue 12, December 2019.

The present work aims at studying the turbulence structure developed over a highly rough bed in open-channel flows (OCFs) by varying the relative submergence through the use of three sediment sizes ranging from gravels to pebbles. The second-order moments were analyzed and compared with those already observed for canonical turbulent OCFs having similar values of relative submergence. Particular attention was paid to the turbulent Reynolds stresses, and the viscous and the form-induced shear stresses in the near bed region. The violation of the Taylor hypothesis was verified through an alternative method, by comparing two time scales, namely, the large scale advection time and the eddy characteristic nonlinear time. Moreover, an analysis of the large eddies was performed with the spectral analysis. The premultiplied spectra provide a way to quantify the contribution of different eddy scales (peaks in the premultiplied spectra) and indicate wavelengths in which a significant amount of energy resides. In order to locate the normalized wavelengths associated with the peaks in the premultiplied spectra, a systematic procedure is presented.

The present work aims at studying the turbulence structure developed over a highly rough bed in open-channel flows (OCFs) by varying the relative submergence through the use of three sediment sizes ranging from gravels to pebbles. The second-order moments were analyzed and compared with those already observed for canonical turbulent OCFs having similar values of relative submergence. Particular attention was paid to the turbulent Reynolds stresses, and the viscous and the form-induced shear stresses in the near bed region. The violation of the Taylor hypothesis was verified through an alternative method, by comparing two time scales, namely, the large scale advection time and the eddy characteristic nonlinear time. Moreover, an analysis of the large eddies was performed with the spectral analysis. The premultiplied spectra provide a way to quantify the contribution of different eddy scales (peaks in the premultiplied spectra) and indicate wavelengths in which a significant amount of energy resides. In order to locate the normalized wavelengths associated with the peaks in the premultiplied spectra, a systematic procedure is presented.

Categories: Latest papers in fluid mechanics

### Single-point structure tensors in turbulent channel flows with smooth and wavy walls

Physics of Fluids, Volume 31, Issue 12, December 2019.

A long-standing problem in turbulence modeling is that the Reynolds stress tensor alone is not necessarily sufficient to characterize the transient and nonequilibrium behaviors of turbulence under arbitrary mean deformation or frame rotation. A more complete single-point characterization of the flow can be obtained using the structure dimensionality, circulicity, and inhomogeneity tensors. These tensors are one-point correlations of local stream vector gradients and carry nonlocal information regarding the structure of the flow field. We explore the potential of these tensors to improve understanding of complex turbulent flows using direct numerical simulation of flows in channels with a smooth wall and a two-dimensional sinusoidal wavy wall. To enforce no-slip and no-penetration conditions at wavy-wall boundaries, an immersed boundary method for the stream vector Poisson equation was adopted within the framework of Stylianou, Pecnik, and Kassinos, “A general framework for computing the turbulence structure tensors,” Comput. Fluids 106, 54–66 (2015). The results show that the effects of wall waviness on the inclination and aspect ratio of the two-point velocity correlation near the wall are reproduced qualitatively by their corresponding single-point tensor representations. In the outer layer, good quantitative agreement is achieved for both parameters. Additional observations on the structural changes of turbulence due to wall waviness and their relevance to turbulence modeling with surface roughness are discussed. The findings of this investigation suggest that single-point structure tensors can be appended to the modeling basis for inhomogeneous flows with geometrically complex boundaries, such as rough-wall flows, to develop improved turbulence models.

A long-standing problem in turbulence modeling is that the Reynolds stress tensor alone is not necessarily sufficient to characterize the transient and nonequilibrium behaviors of turbulence under arbitrary mean deformation or frame rotation. A more complete single-point characterization of the flow can be obtained using the structure dimensionality, circulicity, and inhomogeneity tensors. These tensors are one-point correlations of local stream vector gradients and carry nonlocal information regarding the structure of the flow field. We explore the potential of these tensors to improve understanding of complex turbulent flows using direct numerical simulation of flows in channels with a smooth wall and a two-dimensional sinusoidal wavy wall. To enforce no-slip and no-penetration conditions at wavy-wall boundaries, an immersed boundary method for the stream vector Poisson equation was adopted within the framework of Stylianou, Pecnik, and Kassinos, “A general framework for computing the turbulence structure tensors,” Comput. Fluids 106, 54–66 (2015). The results show that the effects of wall waviness on the inclination and aspect ratio of the two-point velocity correlation near the wall are reproduced qualitatively by their corresponding single-point tensor representations. In the outer layer, good quantitative agreement is achieved for both parameters. Additional observations on the structural changes of turbulence due to wall waviness and their relevance to turbulence modeling with surface roughness are discussed. The findings of this investigation suggest that single-point structure tensors can be appended to the modeling basis for inhomogeneous flows with geometrically complex boundaries, such as rough-wall flows, to develop improved turbulence models.

Categories: Latest papers in fluid mechanics

### A boundary condition for Guderley’s converging shock problem

Physics of Fluids, Volume 31, Issue 12, December 2019.

The Guderley model of a self-similar imploding shock based on the group invariance of the flow equations is a powerful tool in understanding the behavior of converging shock waves. Two modifications described here improve the predictions of observable quantities in spherical-shock wave experiments. First, a noninfinite boundary condition is established by the isentropic release of the outer pressure. Second, a two-temperature system of ions and electrons allows description of higher temperatures while conserving energy and without perturbing the overall hydrodynamics of the solution. These modifications of the Guderley model improve the prediction of the observables in laser driven spherical shock experiments in reference to a one dimensional (1-D) hydrodynamics code.

The Guderley model of a self-similar imploding shock based on the group invariance of the flow equations is a powerful tool in understanding the behavior of converging shock waves. Two modifications described here improve the predictions of observable quantities in spherical-shock wave experiments. First, a noninfinite boundary condition is established by the isentropic release of the outer pressure. Second, a two-temperature system of ions and electrons allows description of higher temperatures while conserving energy and without perturbing the overall hydrodynamics of the solution. These modifications of the Guderley model improve the prediction of the observables in laser driven spherical shock experiments in reference to a one dimensional (1-D) hydrodynamics code.

Categories: Latest papers in fluid mechanics

### On the Holway-Weiss debate: Convergence of the Grad-moment-expansion in kinetic gas theory

Physics of Fluids, Volume 31, Issue 12, December 2019.

Moment expansions are used as a model reduction technique in kinetic gas theory to approximate the Boltzmann equation. Rarefied gas models based on so-called moment equations have become increasingly popular recently. However, in a seminal paper by Holway [“Existence of kinetic theory solutions to the shock structure problem,” Phys. Fluids 7(6), 911–913 (1965)], a fundamental restriction on the existence of the expansion was used to explain subshock behavior of shock profile solutions obtained by moment equations. Later, Weiss [“Comments on ‘Existence of kinetic theory solutions to the shock structure problem’ [Phys. Fluids 7, 911 (1964)],” Phys. Fluids 8(6), 1689–1690 (1996)] argued that this restriction does not exist. We will revisit and discuss their findings and explain that both arguments have a correct and an incorrect part. While a general convergence restriction for moment expansions does exist, it cannot be attributed to subshock solutions. We will also discuss the implications of the restriction and give some numerical evidence for our considerations.

Moment expansions are used as a model reduction technique in kinetic gas theory to approximate the Boltzmann equation. Rarefied gas models based on so-called moment equations have become increasingly popular recently. However, in a seminal paper by Holway [“Existence of kinetic theory solutions to the shock structure problem,” Phys. Fluids 7(6), 911–913 (1965)], a fundamental restriction on the existence of the expansion was used to explain subshock behavior of shock profile solutions obtained by moment equations. Later, Weiss [“Comments on ‘Existence of kinetic theory solutions to the shock structure problem’ [Phys. Fluids 7, 911 (1964)],” Phys. Fluids 8(6), 1689–1690 (1996)] argued that this restriction does not exist. We will revisit and discuss their findings and explain that both arguments have a correct and an incorrect part. While a general convergence restriction for moment expansions does exist, it cannot be attributed to subshock solutions. We will also discuss the implications of the restriction and give some numerical evidence for our considerations.

Categories: Latest papers in fluid mechanics

### On response spectra and Kramers-Kronig relations in superposition rheometry

Physics of Fluids, Volume 31, Issue 12, December 2019.

In a recent paper, we derived expressions for determining the rate-dependent response spectra directly from parallel superposition rheometry data for the case of a certain Lodge-type integral constitutive model. It was shown that, within the confines of linear Yamamoto perturbation theory, the corresponding parallel superposition moduli satisfy the classical Kramers-Kronig relations. Special bases were presented to convert parallel superposition moduli to orthogonal superposition moduli. In the current paper, we obtain similar results for the integral models of Wagner I and, more generally, K-BKZ. These results facilitate the physical interpretation of parallel superposition moduli and direct model-based comparison of parallel and orthogonal superposition moduli in the study of weak nonlinear response.

In a recent paper, we derived expressions for determining the rate-dependent response spectra directly from parallel superposition rheometry data for the case of a certain Lodge-type integral constitutive model. It was shown that, within the confines of linear Yamamoto perturbation theory, the corresponding parallel superposition moduli satisfy the classical Kramers-Kronig relations. Special bases were presented to convert parallel superposition moduli to orthogonal superposition moduli. In the current paper, we obtain similar results for the integral models of Wagner I and, more generally, K-BKZ. These results facilitate the physical interpretation of parallel superposition moduli and direct model-based comparison of parallel and orthogonal superposition moduli in the study of weak nonlinear response.

Categories: Latest papers in fluid mechanics

### Hydrodynamic characteristics in a sheet flow upstream water flow of a circular cylinder

Physics of Fluids, Volume 31, Issue 12, December 2019.

Sheet flow featured with shallow depth on vegetated slopes plays a key role on the dynamics of soil and water loss, yet the hydrodynamic characteristics of sheet flow pasting a vegetation stem simplified by an emergent cylinder have not been revealed. Laboratory flume experiments were conducted to investigate potential effects of a vegetation stem on velocity components, flow vortexes, and shear stress from time-averaged and time-resolved perspectives. Flow fields on the upstream flow of the cylinder at the symmetry plane were captured by using a high precision Particle Image Velocimetry (PIV, 63 pixel/mm) system. Four flow conditions with flow depths from 0.4 to 0.57 cm and cylinder Reynolds number from 2440 to 3806 were selected to fully evaluate the sheet flow condition. Time-averaged hydrodynamic features were analyzed in terms of streamlines, streamwise velocity, wall-normal velocity, and vorticity. Time-resolved features of two velocity components were then analyzed. Joint probability density functions of the two velocity components exhibited asymmetrical bimodal, indicating two preferred flow states occurred frequently, namely, backflow event and downflow event. Subsequently, analyses by linear stochastic estimation showed that the backflow event was induced by a reverse upstream flow starting from the leading edge of the cylinder and penetrating primary horseshoe vortex, which was motivated by the intermediate-flow mode proposed in previous open channel flow. Meanwhile, the downflow event was induced by a portion of fluid that was unable to penetrate the primary horseshoe vortex and then vertically impinged the flume bed, which was motivated by the downflow mode proposed in this study. As the critical hydrodynamic parameter for local scouring, shear stress was finally sketched. It was suggested that soil control measures should be implemented around the vegetation stem with a radius of 0.1D (D is the cylinder diameter), where the maximum shear stress mostly occurs. The newly defined flow mode could provide deeper insights into the mechanisms of sheet flow and promote the practice of soil erosion control on vegetated hillslopes.

Sheet flow featured with shallow depth on vegetated slopes plays a key role on the dynamics of soil and water loss, yet the hydrodynamic characteristics of sheet flow pasting a vegetation stem simplified by an emergent cylinder have not been revealed. Laboratory flume experiments were conducted to investigate potential effects of a vegetation stem on velocity components, flow vortexes, and shear stress from time-averaged and time-resolved perspectives. Flow fields on the upstream flow of the cylinder at the symmetry plane were captured by using a high precision Particle Image Velocimetry (PIV, 63 pixel/mm) system. Four flow conditions with flow depths from 0.4 to 0.57 cm and cylinder Reynolds number from 2440 to 3806 were selected to fully evaluate the sheet flow condition. Time-averaged hydrodynamic features were analyzed in terms of streamlines, streamwise velocity, wall-normal velocity, and vorticity. Time-resolved features of two velocity components were then analyzed. Joint probability density functions of the two velocity components exhibited asymmetrical bimodal, indicating two preferred flow states occurred frequently, namely, backflow event and downflow event. Subsequently, analyses by linear stochastic estimation showed that the backflow event was induced by a reverse upstream flow starting from the leading edge of the cylinder and penetrating primary horseshoe vortex, which was motivated by the intermediate-flow mode proposed in previous open channel flow. Meanwhile, the downflow event was induced by a portion of fluid that was unable to penetrate the primary horseshoe vortex and then vertically impinged the flume bed, which was motivated by the downflow mode proposed in this study. As the critical hydrodynamic parameter for local scouring, shear stress was finally sketched. It was suggested that soil control measures should be implemented around the vegetation stem with a radius of 0.1D (D is the cylinder diameter), where the maximum shear stress mostly occurs. The newly defined flow mode could provide deeper insights into the mechanisms of sheet flow and promote the practice of soil erosion control on vegetated hillslopes.

Categories: Latest papers in fluid mechanics

### Deformation dynamics and breakup criteria of confined fluid threads in motion

Physics of Fluids, Volume 31, Issue 12, December 2019.

Experiments are carried out to study the breakup of moving fluid threads tightly confined in circular microchannels. A configuration with two flow-focusing channel junctions is used to control lengths and deformations of fluid threads at the first and second junctions, respectively. As fluid threads move and deform simultaneously at the second junction, the final outcomes (nonbreakup, single breakup, and double breakup) depend on the combination of three flow rates. The regime diagram for different outcomes is obtained, and the critical geometrical condition for the transition between nonbreakup and breakup is then identified from the deformation dynamics of the neck section. A theoretical analysis is then carried out to predict critical values of characteristic geometries for the transition between nonbreakup and breakup. The predictions of the critical initial thread length and the length of the first thread after breakup show good agreement with experimental measurements.

Experiments are carried out to study the breakup of moving fluid threads tightly confined in circular microchannels. A configuration with two flow-focusing channel junctions is used to control lengths and deformations of fluid threads at the first and second junctions, respectively. As fluid threads move and deform simultaneously at the second junction, the final outcomes (nonbreakup, single breakup, and double breakup) depend on the combination of three flow rates. The regime diagram for different outcomes is obtained, and the critical geometrical condition for the transition between nonbreakup and breakup is then identified from the deformation dynamics of the neck section. A theoretical analysis is then carried out to predict critical values of characteristic geometries for the transition between nonbreakup and breakup. The predictions of the critical initial thread length and the length of the first thread after breakup show good agreement with experimental measurements.

Categories: Latest papers in fluid mechanics

### First-principles magnetization relaxation equation of interacting ferrofluids with applications to magnetoviscous effects

Physics of Fluids, Volume 31, Issue 12, December 2019.

Magnetization relaxation equation (MRE) plays a primary role in numerous phenomena and applications involving ferrofluid dynamics. However, as yet there exist no MREs derived from first principles and applicable to concentrated and strongly interacting ferrofluids. In this paper, we derive a novel MRE based on the projection operator technique. It sufficiently accounts for interparticle correlations beyond the scope of previous models. The MREs by Martsenyuk, Raikher, and Shliomis and by Zubarev and Yushkov (ZY), respectively, for ideal and weakly nonideal (WNI) ferrofluids, are recovered as low-order approximations. We also investigate the magnetoviscous effects. For the first time, we unveil qualitatively the different roles played by short- and long-range interparticle correlations. The long-range correlation effect dominates in a WNI ferrofluid, and both our MRE and the ZY model are in quantitative agreement with simulations on field-dependent rotational viscosity. However, for strongly nonideal ferrofluids, short-range correlations can become substantial and compete with long-range correlations to reduce rotational viscosities. Our MRE is the first dynamic model faithfully capturing both short- and long-range correlations, thereby applicable to ferrofluids characterized by a broad range of concentrations and interacting strengths. It is expected to be a cornerstone for quantitative modeling of the dynamic response of ferrofluids to external fields or flow deformations. Because most commercial ferrofluids are designed to be strongly nonideal to enhance magnetic response, our theory may provide fresh insights for applications of realistic ferrofluids in industry and biomedicine.

Magnetization relaxation equation (MRE) plays a primary role in numerous phenomena and applications involving ferrofluid dynamics. However, as yet there exist no MREs derived from first principles and applicable to concentrated and strongly interacting ferrofluids. In this paper, we derive a novel MRE based on the projection operator technique. It sufficiently accounts for interparticle correlations beyond the scope of previous models. The MREs by Martsenyuk, Raikher, and Shliomis and by Zubarev and Yushkov (ZY), respectively, for ideal and weakly nonideal (WNI) ferrofluids, are recovered as low-order approximations. We also investigate the magnetoviscous effects. For the first time, we unveil qualitatively the different roles played by short- and long-range interparticle correlations. The long-range correlation effect dominates in a WNI ferrofluid, and both our MRE and the ZY model are in quantitative agreement with simulations on field-dependent rotational viscosity. However, for strongly nonideal ferrofluids, short-range correlations can become substantial and compete with long-range correlations to reduce rotational viscosities. Our MRE is the first dynamic model faithfully capturing both short- and long-range correlations, thereby applicable to ferrofluids characterized by a broad range of concentrations and interacting strengths. It is expected to be a cornerstone for quantitative modeling of the dynamic response of ferrofluids to external fields or flow deformations. Because most commercial ferrofluids are designed to be strongly nonideal to enhance magnetic response, our theory may provide fresh insights for applications of realistic ferrofluids in industry and biomedicine.

Categories: Latest papers in fluid mechanics

### Two-liquid electroosmotic thrusters for micro propulsion applications

Physics of Fluids, Volume 31, Issue 12, December 2019.

We investigate analytically the thruster performances and power consumption rates of a two-liquid electroosmotic thruster based on slit microchannels with hydrodynamic slip walls. The two electrolytes are considered to have different material properties and are arranged in the configuration of a core liquid layer surrounded by immiscible outer liquid layers with the outer layers in contact with the microchannel solid walls, thus forming electrical double layers at the solid-liquid interface. Interfacial potential jumps and surface charge densities are included to model the liquid-liquid interfacial double layers. Results reveal that, with the properties of both liquids being identical, nonzero liquid-liquid interfacial electrostatics only slightly increase the thrust but noticeably reduce the thruster efficiency and thrust-to-power ratio due to the enhanced Joule heating and viscous dissipation caused by the increased charge distributions and distorted velocity profiles. Moreover, the thrust and efficiency can be substantially increased as the dynamic viscosity ratio is decreased with the density ratio fixed at one, whereas the thrust, efficiency, and thrust-to-power ratio are all significantly enhanced by increasing the dynamic viscosity ratio when the kinematic viscosity ratio equals to one. The bulk electrolyte concentration/conductivity ratio is identified as a key parameter capable of simultaneously maximizing one or more thruster performances. While improving upon the performances of the single-liquid electroosmotic thruster previously reported, the two-liquid results and modeling presented herein may likely relax the limitations on the choice of electroosmotic propellants, increase the operational flexibility of electrokinetic thrusters, and be further applied in space or underwater micropropulsion applications.

We investigate analytically the thruster performances and power consumption rates of a two-liquid electroosmotic thruster based on slit microchannels with hydrodynamic slip walls. The two electrolytes are considered to have different material properties and are arranged in the configuration of a core liquid layer surrounded by immiscible outer liquid layers with the outer layers in contact with the microchannel solid walls, thus forming electrical double layers at the solid-liquid interface. Interfacial potential jumps and surface charge densities are included to model the liquid-liquid interfacial double layers. Results reveal that, with the properties of both liquids being identical, nonzero liquid-liquid interfacial electrostatics only slightly increase the thrust but noticeably reduce the thruster efficiency and thrust-to-power ratio due to the enhanced Joule heating and viscous dissipation caused by the increased charge distributions and distorted velocity profiles. Moreover, the thrust and efficiency can be substantially increased as the dynamic viscosity ratio is decreased with the density ratio fixed at one, whereas the thrust, efficiency, and thrust-to-power ratio are all significantly enhanced by increasing the dynamic viscosity ratio when the kinematic viscosity ratio equals to one. The bulk electrolyte concentration/conductivity ratio is identified as a key parameter capable of simultaneously maximizing one or more thruster performances. While improving upon the performances of the single-liquid electroosmotic thruster previously reported, the two-liquid results and modeling presented herein may likely relax the limitations on the choice of electroosmotic propellants, increase the operational flexibility of electrokinetic thrusters, and be further applied in space or underwater micropropulsion applications.

Categories: Latest papers in fluid mechanics

### Effects of spatially decaying elastic tension on the instability of viscoelastic jets

Physics of Fluids, Volume 31, Issue 12, December 2019.

This paper theoretically examines the spatial linear instability of viscoelastic jets subjected to unrelaxed axial stress tension and moving within an inviscid stationary gas medium. Unlike the constant value assumption of previous studies, the effects of spatial decaying of the unrelaxed stress tension are included here. The Oldroyd-B constitutive equation has been adopted to model fluid viscoelasticity. Results indicated that the effects of unrelaxed stress tension were complicated and mainly dependent on stress relaxation time. When stress relaxation time was short, the maximum growth rates along the jet decreased to the constant value of the completely relaxed case; increasing unrelaxed tension slightly decreased the breakup length. When the stress relaxation time increased to exceed the critical value, the maximum growth rates continued to increase along the jet and larger unrelaxed tensions caused longer breakup lengths. This twofold effect can be explained by the competition between the stabilizing effects of the unrelaxed tension itself and the destabilizing effects of the spatial decay. Moreover, the fluid elasticity suppressed instability when the unrelaxed tension was great. Responses to the spatial decaying unrelaxed tension of the axisymmetric and nonaxisymmetric disturbances for high-speed viscoelastic jets were similar to those of the capillary case. Generally, the complex effects of the interplay between fluid elasticity and the spatially decaying unrelaxed tension may qualitatively explain the breakup behaviors of viscoelastic jets in experiments.

This paper theoretically examines the spatial linear instability of viscoelastic jets subjected to unrelaxed axial stress tension and moving within an inviscid stationary gas medium. Unlike the constant value assumption of previous studies, the effects of spatial decaying of the unrelaxed stress tension are included here. The Oldroyd-B constitutive equation has been adopted to model fluid viscoelasticity. Results indicated that the effects of unrelaxed stress tension were complicated and mainly dependent on stress relaxation time. When stress relaxation time was short, the maximum growth rates along the jet decreased to the constant value of the completely relaxed case; increasing unrelaxed tension slightly decreased the breakup length. When the stress relaxation time increased to exceed the critical value, the maximum growth rates continued to increase along the jet and larger unrelaxed tensions caused longer breakup lengths. This twofold effect can be explained by the competition between the stabilizing effects of the unrelaxed tension itself and the destabilizing effects of the spatial decay. Moreover, the fluid elasticity suppressed instability when the unrelaxed tension was great. Responses to the spatial decaying unrelaxed tension of the axisymmetric and nonaxisymmetric disturbances for high-speed viscoelastic jets were similar to those of the capillary case. Generally, the complex effects of the interplay between fluid elasticity and the spatially decaying unrelaxed tension may qualitatively explain the breakup behaviors of viscoelastic jets in experiments.

Categories: Latest papers in fluid mechanics

### Effect of porosity on the settling behavior of a 2D elliptic particle in a narrow vessel: A lattice-Boltzmann simulation

Physics of Fluids, Volume 31, Issue 12, December 2019.

Dynamics of a single porous, rigid, two-dimensional (2D) elliptic particle settling in a narrow vertical channel filled with a Newtonian fluid is numerically studied using the lattice-Boltzmann method. The main objective of the work is to investigate the role played by the particle’s permeability on its trajectory, orientation, and terminal velocity when released from the rest state with prescribed initial conditions. Assuming that the flow induced in the fluid surrounding the particle is laminar, incompressible, isothermal, and two-dimensional, numerical results could be obtained over a wide range of parameter settings suggesting that permeability can strongly affect the modes of sedimentation reported in the literature for impermeable elliptic particles provided that the particle’s permeability is larger than a threshold. Above this threshold, permeability is predicted to increase the terminal velocity of the particle with its severity depending on the blockage ratio. It is also predicted that a permeable particle is less sensitive to initial orientation and position as compared with an impermeable particle.

Dynamics of a single porous, rigid, two-dimensional (2D) elliptic particle settling in a narrow vertical channel filled with a Newtonian fluid is numerically studied using the lattice-Boltzmann method. The main objective of the work is to investigate the role played by the particle’s permeability on its trajectory, orientation, and terminal velocity when released from the rest state with prescribed initial conditions. Assuming that the flow induced in the fluid surrounding the particle is laminar, incompressible, isothermal, and two-dimensional, numerical results could be obtained over a wide range of parameter settings suggesting that permeability can strongly affect the modes of sedimentation reported in the literature for impermeable elliptic particles provided that the particle’s permeability is larger than a threshold. Above this threshold, permeability is predicted to increase the terminal velocity of the particle with its severity depending on the blockage ratio. It is also predicted that a permeable particle is less sensitive to initial orientation and position as compared with an impermeable particle.

Categories: Latest papers in fluid mechanics

### Jump phenomena in vortex-induced vibrations of a circular cylinder at a low Reynolds number

Physics of Fluids, Volume 31, Issue 12, December 2019.

The cross flow-induced vibrations of a circular cylinder at the Reynolds number of 150 are numerically investigated in a systematic manner in terms of a wide range of reduced velocity. The effect of the mass ratio on the cylinder behavior is studied, with three mass ratios, namely, 2, 10, and 50, being considered particularly in detail. The mass ratio is defined as the mass of the cylinder to the mass of the fluid it displaces. A sudden decrease in the vibration amplitude takes place at a certain value of the reduced velocity, accompanied by an abrupt increase in the lift coefficient and the vortex shedding frequency. The vortex shedding frequency at the upper end of the lock-in region is about 0.14 for all the mass ratios, which may mark the lower limit of the vortex shedding frequency at this Reynolds number. The jump phenomena may be ascribed to this limitation. Moreover, the vortex shedding frequency in the non-lock-in region varies slightly with the reduced velocity but is not approaching the Strouhal number for the stationary cylinder at the same Reynolds number. In fact, the frequency rises with the increasing mass ratio and reaches about 0.2 as the mass ratio is larger than 10. Besides, the vortex shedding mode does not remain “2S” for the mass ratio larger than 14 when the reduced velocity is increased to get into the non-lock-in region since the vortex shedding frequency is separate from the cylinder oscillation frequency.

The cross flow-induced vibrations of a circular cylinder at the Reynolds number of 150 are numerically investigated in a systematic manner in terms of a wide range of reduced velocity. The effect of the mass ratio on the cylinder behavior is studied, with three mass ratios, namely, 2, 10, and 50, being considered particularly in detail. The mass ratio is defined as the mass of the cylinder to the mass of the fluid it displaces. A sudden decrease in the vibration amplitude takes place at a certain value of the reduced velocity, accompanied by an abrupt increase in the lift coefficient and the vortex shedding frequency. The vortex shedding frequency at the upper end of the lock-in region is about 0.14 for all the mass ratios, which may mark the lower limit of the vortex shedding frequency at this Reynolds number. The jump phenomena may be ascribed to this limitation. Moreover, the vortex shedding frequency in the non-lock-in region varies slightly with the reduced velocity but is not approaching the Strouhal number for the stationary cylinder at the same Reynolds number. In fact, the frequency rises with the increasing mass ratio and reaches about 0.2 as the mass ratio is larger than 10. Besides, the vortex shedding mode does not remain “2S” for the mass ratio larger than 14 when the reduced velocity is increased to get into the non-lock-in region since the vortex shedding frequency is separate from the cylinder oscillation frequency.

Categories: Latest papers in fluid mechanics

### Rotor boundary layer development in a two-stage compressor

Physics of Fluids, Volume 31, Issue 12, December 2019.

This experimental study provides striking examples of the complex flow and turbulence structures resulting from blade–wake and wake–wake interactions in a multistage turbomachine. Particle image velocimetry measurements were performed within the second-stage rotors of a two-stage compressor. The first-stage stator wake is distorted and produces a kink structure in the second-stage rotor blades passage. This kink, also called a turbulent hot spot, with concentrated vorticity, high turbulence levels, and high turbulence kinetic energy, is caused by the interaction between the first-stage rotor wake and the stator wake. A high-speed region and a low-speed region are observed around the turbulent hot spot. The perturbation velocity is counterclockwise around the turbulent hot spot, with a magnitude much larger than that in the wake. The turbulent hot spot is more unstable and active than the wake and, thus, might play a pivotal role in the passage flow. The high turbulence and the negative jet behavior of the wake dominate the interaction between the unsteady wake and the separated boundary layer on the suction surface of the blade. When the upstream wake impinges on the blade, the boundary layer thickness first increases owing to the presence of the negative jet, and a thickened boundary layer region in the form of a turbulent spot is formed because of the high turbulence intensity in the wake. Then, the boundary layer gradually becomes thinner because of the presence of a calmed region that follows the thickened boundary layer region. Finally, the boundary layer gradually thickens again and recovers to separation. Thus, the boundary layer thickness is periodic in a wake passing cycle.

This experimental study provides striking examples of the complex flow and turbulence structures resulting from blade–wake and wake–wake interactions in a multistage turbomachine. Particle image velocimetry measurements were performed within the second-stage rotors of a two-stage compressor. The first-stage stator wake is distorted and produces a kink structure in the second-stage rotor blades passage. This kink, also called a turbulent hot spot, with concentrated vorticity, high turbulence levels, and high turbulence kinetic energy, is caused by the interaction between the first-stage rotor wake and the stator wake. A high-speed region and a low-speed region are observed around the turbulent hot spot. The perturbation velocity is counterclockwise around the turbulent hot spot, with a magnitude much larger than that in the wake. The turbulent hot spot is more unstable and active than the wake and, thus, might play a pivotal role in the passage flow. The high turbulence and the negative jet behavior of the wake dominate the interaction between the unsteady wake and the separated boundary layer on the suction surface of the blade. When the upstream wake impinges on the blade, the boundary layer thickness first increases owing to the presence of the negative jet, and a thickened boundary layer region in the form of a turbulent spot is formed because of the high turbulence intensity in the wake. Then, the boundary layer gradually becomes thinner because of the presence of a calmed region that follows the thickened boundary layer region. Finally, the boundary layer gradually thickens again and recovers to separation. Thus, the boundary layer thickness is periodic in a wake passing cycle.

Categories: Latest papers in fluid mechanics

### Turbulence statistics and very-large-scale motions in decelerating open-channel flow

Physics of Fluids, Volume 31, Issue 12, December 2019.

This study experimentally examined the turbulent characteristics of decelerating open-channel flow based on particle imaging velocimetry measurement. The decelerating flow shows a similar velocity profile to that in uniform flow, but it exhibits greater turbulence intensity and Reynolds stress. Statistical evidence of the presence of very-large-scale motions (VLSMs) in decelerating open-channel flows was presented for the first time. The results indicate that VLSMs in decelerating flows can survive further away from the wall when compared to other wall-turbulence flows. The contribution rate of the VLSMs to the turbulent kinetic energy and the Reynolds stress in the decelerating open-channel flow is slightly lower than that in channels, boundary layers, and pipe flows.

This study experimentally examined the turbulent characteristics of decelerating open-channel flow based on particle imaging velocimetry measurement. The decelerating flow shows a similar velocity profile to that in uniform flow, but it exhibits greater turbulence intensity and Reynolds stress. Statistical evidence of the presence of very-large-scale motions (VLSMs) in decelerating open-channel flows was presented for the first time. The results indicate that VLSMs in decelerating flows can survive further away from the wall when compared to other wall-turbulence flows. The contribution rate of the VLSMs to the turbulent kinetic energy and the Reynolds stress in the decelerating open-channel flow is slightly lower than that in channels, boundary layers, and pipe flows.

Categories: Latest papers in fluid mechanics

### Large eddy simulations of a turbulent channel flow with a deforming wall undergoing high steepness traveling waves

Physics of Fluids, Volume 31, Issue 12, December 2019.

Backward traveling waves over a wall of a fully developed turbulent channel are known to reduce the drag coefficient, flow separation, and turbulence intensity. Based on previous studies of traveling waves with a small steepness (s = a/λ < 0.0625, a: nondimensional amplitude, λ: nondimensional wavelength), it is thought that the nondimensional wave-speed (C = C*/U*, C*: dimensional wave-speed, U*: mean channel velocity) is required to be more than one to have a zero net drag and a high reduction in the turbulent kinetic energy (TKE). This idea is tested here for waves with higher wave steepness (0.05 < s < 0.15) at various wave-speeds using large eddy simulations of a fully developed turbulent channel in which one wall is undergoing a traveling wave. It is found that the increase in wave steepness decreases the wave-speed at which a net zero drag is obtained, e.g., for waves with steepness of s = 0.05, 0.075, and 0.15, the wave-speed is, approximately, C = 1.6 ± 0.1, 0.9 ± 0.1, and 0.7 ± 0.1, respectively. Similarly, the increase in wave steepness decreases the wave-speed at which TKE of the flow in the vicinity of the wave is highly reduced, e.g., qualitatively minimized. In fact, the wave-speeds at which the high reduction in TKE is observed in this study are C = 1.2, 1.2, and 0.6 for waves with wave steepness of 0.05, 0.075, and 0.15, respectively.

Backward traveling waves over a wall of a fully developed turbulent channel are known to reduce the drag coefficient, flow separation, and turbulence intensity. Based on previous studies of traveling waves with a small steepness (s = a/λ < 0.0625, a: nondimensional amplitude, λ: nondimensional wavelength), it is thought that the nondimensional wave-speed (C = C*/U*, C*: dimensional wave-speed, U*: mean channel velocity) is required to be more than one to have a zero net drag and a high reduction in the turbulent kinetic energy (TKE). This idea is tested here for waves with higher wave steepness (0.05 < s < 0.15) at various wave-speeds using large eddy simulations of a fully developed turbulent channel in which one wall is undergoing a traveling wave. It is found that the increase in wave steepness decreases the wave-speed at which a net zero drag is obtained, e.g., for waves with steepness of s = 0.05, 0.075, and 0.15, the wave-speed is, approximately, C = 1.6 ± 0.1, 0.9 ± 0.1, and 0.7 ± 0.1, respectively. Similarly, the increase in wave steepness decreases the wave-speed at which TKE of the flow in the vicinity of the wave is highly reduced, e.g., qualitatively minimized. In fact, the wave-speeds at which the high reduction in TKE is observed in this study are C = 1.2, 1.2, and 0.6 for waves with wave steepness of 0.05, 0.075, and 0.15, respectively.

Categories: Latest papers in fluid mechanics

### Direct numerical simulation of a tip-leakage flow in a planar duct with a longitudinal slit

Physics of Fluids, Volume 31, Issue 12, December 2019.

A planar duct flow configuration with a cross-flow injected from a longitudinal slit close to the upper wall of the duct is studied by using a direct numerical simulation approach to explore the underlying flow mechanism in relation to the tip-leakage vortex (TLV), which is one of the most important flow phenomena in turbomachinery. Major characteristics of TLV in a rotor of turbomachinery are identified in the current flow model. The analysis of mean and instantaneous flow fields reveals that the interaction between the main (axial) flow and jet (cross) flow is the primary source of the generation of the TLV. The evolution of the TLV is then investigated, and a vortex breakup phenomenon is identified. The evolution of TLV can be divided into three phases, i.e., the formation phase, the breakup phase, and the diffusion phase. Mean streamlines and turbulence kinetic energy (TKE) budgets are analyzed, showing that the high TKE central spot in the formation phase is due to the interaction between highly swirling vortex filaments and mean velocity gradient. In the outer part of the TLV, the TKE is mainly produced in the shear-layer and transported toward the center by the turbulence transport.

A planar duct flow configuration with a cross-flow injected from a longitudinal slit close to the upper wall of the duct is studied by using a direct numerical simulation approach to explore the underlying flow mechanism in relation to the tip-leakage vortex (TLV), which is one of the most important flow phenomena in turbomachinery. Major characteristics of TLV in a rotor of turbomachinery are identified in the current flow model. The analysis of mean and instantaneous flow fields reveals that the interaction between the main (axial) flow and jet (cross) flow is the primary source of the generation of the TLV. The evolution of the TLV is then investigated, and a vortex breakup phenomenon is identified. The evolution of TLV can be divided into three phases, i.e., the formation phase, the breakup phase, and the diffusion phase. Mean streamlines and turbulence kinetic energy (TKE) budgets are analyzed, showing that the high TKE central spot in the formation phase is due to the interaction between highly swirling vortex filaments and mean velocity gradient. In the outer part of the TLV, the TKE is mainly produced in the shear-layer and transported toward the center by the turbulence transport.

Categories: Latest papers in fluid mechanics

### Geometry effects on mean wake topology and large-scale coherent structures of wall-mounted prisms

Physics of Fluids, Volume 31, Issue 12, December 2019.

Turbulent wake behind five wall-mounted rectangular prisms is measured by time-resolved particle-image velocimetry with an aim to generalize the effects of prism geometry (in terms of aspect ratio, AR, and side ratio, SR) on the wake characteristics. For the time-averaged wake, the arch-type topology is well supported. With AR increasing from 1 to 4 for the square prisms, a transition process between the “dipole” and “quadrupole” wake patterns is observed. On the other hand, an increase in SR does not seem to greatly influence the mean wake structure behind rectangular prisms unless reattachment occurs on the side walls. The turbulent wake velocity fields are analyzed with a proper orthogonal decomposition method, considering the intrinsic symmetries of vortex shedding activities. In the extraction of dominant low-order flow structures, the low-frequency shift mode and periodic vortex shedding mode pair are always captured as the most important turbulent kinetic energy contributors but with significant nonlinear cross-superposition. A low-pass Gaussian filter is then introduced to achieve separation between these two types of coherent structures via new spatial modes, which maintain the same mode shape patterns. The size of the shift mode vortex is found closely related to the time-averaged wake structure, while the pattern of the Karman vortex shedding mode pair seems completely independent. The two separated pure modes develop continuously and compete with each other along the model height. The present study appears to be the first one to investigate the effects of prism geometry on large-scale coherent wake motions from this perspective.

Turbulent wake behind five wall-mounted rectangular prisms is measured by time-resolved particle-image velocimetry with an aim to generalize the effects of prism geometry (in terms of aspect ratio, AR, and side ratio, SR) on the wake characteristics. For the time-averaged wake, the arch-type topology is well supported. With AR increasing from 1 to 4 for the square prisms, a transition process between the “dipole” and “quadrupole” wake patterns is observed. On the other hand, an increase in SR does not seem to greatly influence the mean wake structure behind rectangular prisms unless reattachment occurs on the side walls. The turbulent wake velocity fields are analyzed with a proper orthogonal decomposition method, considering the intrinsic symmetries of vortex shedding activities. In the extraction of dominant low-order flow structures, the low-frequency shift mode and periodic vortex shedding mode pair are always captured as the most important turbulent kinetic energy contributors but with significant nonlinear cross-superposition. A low-pass Gaussian filter is then introduced to achieve separation between these two types of coherent structures via new spatial modes, which maintain the same mode shape patterns. The size of the shift mode vortex is found closely related to the time-averaged wake structure, while the pattern of the Karman vortex shedding mode pair seems completely independent. The two separated pure modes develop continuously and compete with each other along the model height. The present study appears to be the first one to investigate the effects of prism geometry on large-scale coherent wake motions from this perspective.

Categories: Latest papers in fluid mechanics

### Investigation of fluctuating characteristics of wall shear stress in supersonic flow

Physics of Fluids, Volume 31, Issue 12, December 2019.

The characteristics of the flow structure and wall shear stress (WSS) in a hydrogen-fueled scramjet were investigated. A microelectromechanical system-based sensor was used for measuring the WSS. The flow structure was found to be stable in both nonreacting and reacting flows. The expansion waves near the cavity step that occurred in a nonreacting flow were transformed to oblique shock waves owing to hydrogen combustion, and the cavity shear layer was lifted into the core flow. The flame was in the cavity shear layer and the wall boundary layer near the top wall. The time-averaged value (TAV) of the WSS in the isolator was about 825.6 Pa, and the flow was turbulent. The intensity of WSS fluctuations was about 21.5%, and the probability density function of the WSS was negatively skewed in a nonreacting flow. The TAV of the WSS decreased from 370 Pa to 269.5 Pa in the combustor after combustion occurred. This was because the velocity gradient was decreased in the combustion flow. The intensity of WSS fluctuations was increased by the hydrogen combustion.

The characteristics of the flow structure and wall shear stress (WSS) in a hydrogen-fueled scramjet were investigated. A microelectromechanical system-based sensor was used for measuring the WSS. The flow structure was found to be stable in both nonreacting and reacting flows. The expansion waves near the cavity step that occurred in a nonreacting flow were transformed to oblique shock waves owing to hydrogen combustion, and the cavity shear layer was lifted into the core flow. The flame was in the cavity shear layer and the wall boundary layer near the top wall. The time-averaged value (TAV) of the WSS in the isolator was about 825.6 Pa, and the flow was turbulent. The intensity of WSS fluctuations was about 21.5%, and the probability density function of the WSS was negatively skewed in a nonreacting flow. The TAV of the WSS decreased from 370 Pa to 269.5 Pa in the combustor after combustion occurred. This was because the velocity gradient was decreased in the combustion flow. The intensity of WSS fluctuations was increased by the hydrogen combustion.

Categories: Latest papers in fluid mechanics

### Super-resolution reconstruction of turbulent velocity fields using a generative adversarial network-based artificial intelligence framework

Physics of Fluids, Volume 31, Issue 12, December 2019.

A general super-resolution reconstruction strategy was proposed for turbulent velocity fields using a generative adversarial network-based artificial intelligence framework. Two advanced neural networks, i.e., super-resolution generative adversarial network (SRGAN) and enhanced-SRGAN (ESRGAN), were first applied in fluid mechanics to augment the spatial resolution of turbulent flow. As a validation, the flow around a single-cylinder and a more complicated wake flow behind two side-by-side cylinders were experimentally measured using particle image velocimetry. The spatial resolution of the coarse flow field can be successfully augmented by 42 and 82 times with remarkable accuracy. The reconstruction performances of SRGAN and ESRGAN were comprehensively investigated and compared, including an analysis of the recovered instantaneous flow field, statistical flow quantities, and spatial correlations. The results convincingly demonstrated that both models can reconstruct the high-spatial-resolution flow field accurately even in an intricate flow configuration, and ESRGAN can provide a better reconstruction result than SRGAN in the mean and fluctuation flow field.

A general super-resolution reconstruction strategy was proposed for turbulent velocity fields using a generative adversarial network-based artificial intelligence framework. Two advanced neural networks, i.e., super-resolution generative adversarial network (SRGAN) and enhanced-SRGAN (ESRGAN), were first applied in fluid mechanics to augment the spatial resolution of turbulent flow. As a validation, the flow around a single-cylinder and a more complicated wake flow behind two side-by-side cylinders were experimentally measured using particle image velocimetry. The spatial resolution of the coarse flow field can be successfully augmented by 42 and 82 times with remarkable accuracy. The reconstruction performances of SRGAN and ESRGAN were comprehensively investigated and compared, including an analysis of the recovered instantaneous flow field, statistical flow quantities, and spatial correlations. The results convincingly demonstrated that both models can reconstruct the high-spatial-resolution flow field accurately even in an intricate flow configuration, and ESRGAN can provide a better reconstruction result than SRGAN in the mean and fluctuation flow field.

Categories: Latest papers in fluid mechanics