# Physics of Fluids

Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.

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### Algebraic non-equilibrium wall-stress modeling for large eddy simulation based on analytical integration of the thin boundary-layer equation

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

An algebraic nonequilibrium wall-stress model for large eddy simulation is discussed. The ordinary differential equation (ODE) derived from the thin-layer approximated momentum equation, including the temporal, convection, and pressure gradient terms, is considered to form the wall-stress model. Based on the concept of the analytical wall function (AWF) for Reynolds-averaged turbulence models, the profile of the subgrid scale (SGS) eddy viscosity inside the wall-adjacent cells is modeled as a two-segment piecewise linear variations. This simplification makes it possible to analytically integrate the ODE near the wall to algebraically give the wall shear stress as the wall boundary condition for the momentum equation. By applying such integration to the wall-normal velocity component, the methodology to avoid the log-layer mismatch is also presented. Coupled with the standard Smagorinsky model, the proposed SGS-AWF shows good performance in turbulent channel flows at Reτ = 1000–5000 irrespective of the grid resolutions. This SGS-AWF is also confirmed to be superior to the traditional equilibrium wall-stress model in a turbulent backward-facing step flow.

An algebraic nonequilibrium wall-stress model for large eddy simulation is discussed. The ordinary differential equation (ODE) derived from the thin-layer approximated momentum equation, including the temporal, convection, and pressure gradient terms, is considered to form the wall-stress model. Based on the concept of the analytical wall function (AWF) for Reynolds-averaged turbulence models, the profile of the subgrid scale (SGS) eddy viscosity inside the wall-adjacent cells is modeled as a two-segment piecewise linear variations. This simplification makes it possible to analytically integrate the ODE near the wall to algebraically give the wall shear stress as the wall boundary condition for the momentum equation. By applying such integration to the wall-normal velocity component, the methodology to avoid the log-layer mismatch is also presented. Coupled with the standard Smagorinsky model, the proposed SGS-AWF shows good performance in turbulent channel flows at Reτ = 1000–5000 irrespective of the grid resolutions. This SGS-AWF is also confirmed to be superior to the traditional equilibrium wall-stress model in a turbulent backward-facing step flow.

Categories: Latest papers in fluid mechanics

### Understanding the secondary separation from an inclined square cylinder with sharp and rounded trailing edges

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

The steady separated flow past a square cylinder at 45° incidence and having a sharp/rounded base is a unique kind of separated flow around a symmetric bluff obstacle. At low Reynolds numbers (Re ≈ 6–8), this flow displays diverse features that are not known to be displayed by common symmetric bluff bodies, such as circular/square cylinders at zero incidence. The uniqueness of this flow was first highlighted by Kumar et al. [“Steady separation of flow from an inclined square cylinder with sharp and rounded base,” Comput. Fluids 171, 29–40 (2018)] in their recent numerical investigation concerning the onset of initial separation. They reported detailed flow kinematics resulting from separation of the laminar boundary layer via secondary mode, primary mode, and their combination. In this work, based on stabilized finite-element computations, the fluid dynamic aspects of primary and secondary separation are delved. The parameters considered are the normalized corner radius at the cylinder base and Re. Exploration of the influence of base radius on the occurrence/absence of the secondary separation is the main objective. The occurrence of secondary separation is a function of base radius. It occurs only with small or no rounding at the base, i.e., when the pressure gradient close to the base is favorable or mildly adverse. Irrespective of the base radius, the onset of secondary separation occurs at a constant Re value of 7.3. The drag decays as Re−0.62; it becomes invariant when Re is held constant. A new nondimensional parameter η accommodating the effects of pressure recovery and radius of curvature is introduced. The drag exhibits no sensitivity to η.

The steady separated flow past a square cylinder at 45° incidence and having a sharp/rounded base is a unique kind of separated flow around a symmetric bluff obstacle. At low Reynolds numbers (Re ≈ 6–8), this flow displays diverse features that are not known to be displayed by common symmetric bluff bodies, such as circular/square cylinders at zero incidence. The uniqueness of this flow was first highlighted by Kumar et al. [“Steady separation of flow from an inclined square cylinder with sharp and rounded base,” Comput. Fluids 171, 29–40 (2018)] in their recent numerical investigation concerning the onset of initial separation. They reported detailed flow kinematics resulting from separation of the laminar boundary layer via secondary mode, primary mode, and their combination. In this work, based on stabilized finite-element computations, the fluid dynamic aspects of primary and secondary separation are delved. The parameters considered are the normalized corner radius at the cylinder base and Re. Exploration of the influence of base radius on the occurrence/absence of the secondary separation is the main objective. The occurrence of secondary separation is a function of base radius. It occurs only with small or no rounding at the base, i.e., when the pressure gradient close to the base is favorable or mildly adverse. Irrespective of the base radius, the onset of secondary separation occurs at a constant Re value of 7.3. The drag decays as Re−0.62; it becomes invariant when Re is held constant. A new nondimensional parameter η accommodating the effects of pressure recovery and radius of curvature is introduced. The drag exhibits no sensitivity to η.

Categories: Latest papers in fluid mechanics

### Wake-induced vibration of a circular cylinder at a low Reynolds number of 100

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

Wake-induced vibration (WIV) of a circular cylinder in the wake of a stationary bluff body at a low Reynolds number of 100 is numerically investigated in this work. Square prism, rectangular plate, and triangular prism with the same projected width as the diameter of the circular cylinder are employed as the upstream bluff body to examine the effect of obstacle’s shape on the wake interference and WIV. The downstream circular cylinder is allowed to oscillate in both inline and crossflow directions. Three spacing ratios of 2, 4, and 6 are considered in the computations that carried out for a wide range of reduced velocities (Ur = 2–20). In terms of shear layer reattachment, vortex impingement, and wake interference, three distinct flow regimes are identified for the upstream-stationary-downstream-vibrating tandem cylinders, i.e., continuous reattachment regime, alternating reattachment regime, and coshedding regime. The wake flow pattern is sensitive to the spacing ratio and the reduced velocity. Due to the vigorous streamwise response, the gap between the tandem cylinders varies over time and hence the switching of wake regime. Both the hydrodynamic forces and vibration response are tightly associated with the wake interaction. Among the three configurations, the cylinder behind a square prism possesses the largest cross-flow amplitude, while the cylinder behind a plate and that behind a triangular prism present more oscillating characteristics in the response amplitude, due mainly to the unstable and irregular vortex evolution.

Wake-induced vibration (WIV) of a circular cylinder in the wake of a stationary bluff body at a low Reynolds number of 100 is numerically investigated in this work. Square prism, rectangular plate, and triangular prism with the same projected width as the diameter of the circular cylinder are employed as the upstream bluff body to examine the effect of obstacle’s shape on the wake interference and WIV. The downstream circular cylinder is allowed to oscillate in both inline and crossflow directions. Three spacing ratios of 2, 4, and 6 are considered in the computations that carried out for a wide range of reduced velocities (Ur = 2–20). In terms of shear layer reattachment, vortex impingement, and wake interference, three distinct flow regimes are identified for the upstream-stationary-downstream-vibrating tandem cylinders, i.e., continuous reattachment regime, alternating reattachment regime, and coshedding regime. The wake flow pattern is sensitive to the spacing ratio and the reduced velocity. Due to the vigorous streamwise response, the gap between the tandem cylinders varies over time and hence the switching of wake regime. Both the hydrodynamic forces and vibration response are tightly associated with the wake interaction. Among the three configurations, the cylinder behind a square prism possesses the largest cross-flow amplitude, while the cylinder behind a plate and that behind a triangular prism present more oscillating characteristics in the response amplitude, due mainly to the unstable and irregular vortex evolution.

Categories: Latest papers in fluid mechanics

### Lift force acting on a pair of clean bubbles rising in-line

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

In this study, we experimentally observed the motion of a pair of bubbles initially positioned in line, especially focusing on the intermediate Reynolds number case, i.e., 20 < Re < 60. We observed three types of motion at different Reynolds numbers. At a low Reynolds number (Re < 20), the trailing bubble collided with the leading bubble like a pair of rigid spheres. At a high Reynolds number (100 < Re), the trailing bubble moved out from the original vertical line joining the two bubbles. At intermediate Reynolds numbers (20 < Re < 60), small differences in bubble size affected the motion. When the leading bubble was larger than or equal to the trailing bubble, the trailing bubble first approached the leading bubble and later moved out from the initial vertical line owing to a lift force. When the leading bubble was smaller than the trailing bubble, the trailing bubble first approached the leading bubble, and then a repulsive force acted on both bubbles so that both of them moved out from the vertical line in opposite directions. These motions are attributed to two effects, the first is potential effects at short distance between bubbles, and the second is the wake of the leading bubble.

In this study, we experimentally observed the motion of a pair of bubbles initially positioned in line, especially focusing on the intermediate Reynolds number case, i.e., 20 < Re < 60. We observed three types of motion at different Reynolds numbers. At a low Reynolds number (Re < 20), the trailing bubble collided with the leading bubble like a pair of rigid spheres. At a high Reynolds number (100 < Re), the trailing bubble moved out from the original vertical line joining the two bubbles. At intermediate Reynolds numbers (20 < Re < 60), small differences in bubble size affected the motion. When the leading bubble was larger than or equal to the trailing bubble, the trailing bubble first approached the leading bubble and later moved out from the initial vertical line owing to a lift force. When the leading bubble was smaller than the trailing bubble, the trailing bubble first approached the leading bubble, and then a repulsive force acted on both bubbles so that both of them moved out from the vertical line in opposite directions. These motions are attributed to two effects, the first is potential effects at short distance between bubbles, and the second is the wake of the leading bubble.

Categories: Latest papers in fluid mechanics

### Detour induced by the piston effect in the oscillatory double-diffusive convection of a near-critical fluid

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

The nonlinear oscillatory double-diffusive convection in a thermodynamically near-critical binary fluid layer is investigated to explore the interactions between the piston effect and natural convection in the presence of subcritical bifurcation. The bifurcation diagram of the system is studied. Two subcritical bifurcation branches are depicted, which, together with the trivial branch of pure diffusion, are connected by two hysteresis loops. To understand the role of the piston effect, the Boussinesq counterpart of the near-critical system is considered and compared. Results show that the onset of convection is significantly altered by the piston effect. For the Boussinesq system, the lower boundary layer becomes unstable, brings on finite-amplitude perturbations, and leads to a statistically steady state. However, the near-critical system features a two-stage evolution. In the first stage, the lower boundary layer becomes unstable and then returns to stability. As soon as the temperature field relaxes into the second stage, a change of criterion occurs, and the fluid becomes unstable again. The residual convection motions amplify and finally result in finite-amplitude convection. By this means, the near-critical system becomes insensitive to the existence of the higher equilibrium state in hysteresis loops, and detours relative to the Boussinesq system are observed. This paper gives new insights into the piston effect and its interactions with natural convection from a dynamic system point of view. The conclusions can be extended to other situations where subcritical bifurcations exist.

The nonlinear oscillatory double-diffusive convection in a thermodynamically near-critical binary fluid layer is investigated to explore the interactions between the piston effect and natural convection in the presence of subcritical bifurcation. The bifurcation diagram of the system is studied. Two subcritical bifurcation branches are depicted, which, together with the trivial branch of pure diffusion, are connected by two hysteresis loops. To understand the role of the piston effect, the Boussinesq counterpart of the near-critical system is considered and compared. Results show that the onset of convection is significantly altered by the piston effect. For the Boussinesq system, the lower boundary layer becomes unstable, brings on finite-amplitude perturbations, and leads to a statistically steady state. However, the near-critical system features a two-stage evolution. In the first stage, the lower boundary layer becomes unstable and then returns to stability. As soon as the temperature field relaxes into the second stage, a change of criterion occurs, and the fluid becomes unstable again. The residual convection motions amplify and finally result in finite-amplitude convection. By this means, the near-critical system becomes insensitive to the existence of the higher equilibrium state in hysteresis loops, and detours relative to the Boussinesq system are observed. This paper gives new insights into the piston effect and its interactions with natural convection from a dynamic system point of view. The conclusions can be extended to other situations where subcritical bifurcations exist.

Categories: Latest papers in fluid mechanics

### On the origin and structure of a stationary circular hydraulic jump

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

To elucidate the role played by surface tension on the formation and on the structure of a circular hydraulic jump, the results from three different approaches are compared: the shallow-water (SW) equations without considering surface tension effects, the depth-averaged model (DAM) of the SW equations for a flow with a parabolic velocity profile, and the numerical solutions of the full Navier-Stokes (NS) equations, both considering the effect of surface tension and neglecting it. From the SW equations, the jump can be interpreted as a transition region between two solutions of the DAM, with the jump’s location virtually coinciding with a singularity of the DAM’s solution, associated with the inner edge of a recirculation region near the bottom. The jump’s radius and the flow structure upstream of the jump obtained from the NS simulations practically coincide with the results from the SW equations for any flow rate, liquid properties, and downstream boundary conditions, being practically independent of surface tension. However, the structure of the flow downstream of the jump predicted by the SW equations is quite different from the stationary flow resulting from the NS simulations, which strongly depends on surface tension and on the downstream boundary conditions (radius of the disk). One of the main findings of the present work is that no stationary and axisymmetric circular hydraulic jump is found from the NS simulations above a critical value of the surface tension, which depends on the flow conditions, fluid properties, and downstream conditions.

To elucidate the role played by surface tension on the formation and on the structure of a circular hydraulic jump, the results from three different approaches are compared: the shallow-water (SW) equations without considering surface tension effects, the depth-averaged model (DAM) of the SW equations for a flow with a parabolic velocity profile, and the numerical solutions of the full Navier-Stokes (NS) equations, both considering the effect of surface tension and neglecting it. From the SW equations, the jump can be interpreted as a transition region between two solutions of the DAM, with the jump’s location virtually coinciding with a singularity of the DAM’s solution, associated with the inner edge of a recirculation region near the bottom. The jump’s radius and the flow structure upstream of the jump obtained from the NS simulations practically coincide with the results from the SW equations for any flow rate, liquid properties, and downstream boundary conditions, being practically independent of surface tension. However, the structure of the flow downstream of the jump predicted by the SW equations is quite different from the stationary flow resulting from the NS simulations, which strongly depends on surface tension and on the downstream boundary conditions (radius of the disk). One of the main findings of the present work is that no stationary and axisymmetric circular hydraulic jump is found from the NS simulations above a critical value of the surface tension, which depends on the flow conditions, fluid properties, and downstream conditions.

Categories: Latest papers in fluid mechanics

### Time-resolved turbulent velocity field reconstruction using a long short-term memory (LSTM)-based artificial intelligence framework

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

This paper focuses on the time-resolved turbulent flow reconstruction from discrete point measurements and non-time-resolved (non-TR) particle image velocimetry (PIV) measurements using an artificial intelligence framework based on long short-term memory (LSTM). To this end, an LSTM-based proper orthogonal decomposition (POD) model is proposed to establish the relationship between velocity signals and time-varying POD coefficients obtained from non-TR-PIV measurements. An inverted flag flow at Re = 6200 was experimentally measured using TR-PIV at a sampling rate of 2000 Hz for the construction of training and testing datasets and for validation. Two different time-step configurations were employed to investigate the robustness and learning ability of the LSTM-based POD model: a single-time-step structure and a multi-time-step structure. The results demonstrate that the LSTM-based POD model has great potential for time-series reconstruction since it can successfully recover the temporal revolution of POD coefficients with remarkable accuracy, even in high-order POD modes. The time-resolved flow fields can be reconstructed well using coefficients obtained from the proposed model. In addition, a relative error reconstruction analysis was conducted to compare the performance of different time-step configurations further, and the results demonstrated that the POD model with multi-time-step structure provided better reconstruction of the flow fields.

This paper focuses on the time-resolved turbulent flow reconstruction from discrete point measurements and non-time-resolved (non-TR) particle image velocimetry (PIV) measurements using an artificial intelligence framework based on long short-term memory (LSTM). To this end, an LSTM-based proper orthogonal decomposition (POD) model is proposed to establish the relationship between velocity signals and time-varying POD coefficients obtained from non-TR-PIV measurements. An inverted flag flow at Re = 6200 was experimentally measured using TR-PIV at a sampling rate of 2000 Hz for the construction of training and testing datasets and for validation. Two different time-step configurations were employed to investigate the robustness and learning ability of the LSTM-based POD model: a single-time-step structure and a multi-time-step structure. The results demonstrate that the LSTM-based POD model has great potential for time-series reconstruction since it can successfully recover the temporal revolution of POD coefficients with remarkable accuracy, even in high-order POD modes. The time-resolved flow fields can be reconstructed well using coefficients obtained from the proposed model. In addition, a relative error reconstruction analysis was conducted to compare the performance of different time-step configurations further, and the results demonstrated that the POD model with multi-time-step structure provided better reconstruction of the flow fields.

Categories: Latest papers in fluid mechanics

### Combining particle-in-cell and direct simulation Monte Carlo for the simulation of reactive plasma flows

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

A combined approach for the simulation of reactive, neutral, partially or fully ionized plasma flows is presented. This is realized in a code framework named “PICLas” for the approximate solution of the Boltzmann equation by particle based methods. PICLas combines the particle-in-cell method for the collisionless Vlasov–Maxwell system and the direct simulation Monte Carlo method for neutral reactive flows. Basic physical and mathematical modeling of both methods is addressed, and some application examples are presented in order to demonstrate the capabilities and the broad applicability of the solution strategy.

A combined approach for the simulation of reactive, neutral, partially or fully ionized plasma flows is presented. This is realized in a code framework named “PICLas” for the approximate solution of the Boltzmann equation by particle based methods. PICLas combines the particle-in-cell method for the collisionless Vlasov–Maxwell system and the direct simulation Monte Carlo method for neutral reactive flows. Basic physical and mathematical modeling of both methods is addressed, and some application examples are presented in order to demonstrate the capabilities and the broad applicability of the solution strategy.

Categories: Latest papers in fluid mechanics

### Aspect ratio dependence of Rayleigh-Bénard convection of cold water near its maximum density in box-shaped containers

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

The aim of this research is to understand the effect of the aspect ratio on the heat transfer ability and hydrodynamics characteristics of Rayleigh-Bénard convection of cold water near its maximum density in box-shaped containers. The Rayleigh number is fixed at 109, density inversion parameters are 0.3, 0.5 and 0.7, and the aspect ratio ranges from 1/60 to 1. Results indicate that the average Nusselt number presents a weak dependence on the aspect ratio at the large aspect ratio (A > 0.3). However, it reaches the maximum and then drops when the aspect ratio decreases from A = 0.3. Large scale circulations are observed for containers at the large aspect ratio, and the confinement of sidewalls weakens the large-scale circulation and eventually destructs it. At the large aspect ratio, the velocity fluctuation near the sidewalls is stronger than that in the center zone, because plumes primarily move along the sidewalls of the container. At a small aspect ratio, more plumes appear in the center of the container, where the fluctuation is stronger than that near sidewalls. The effect of cold plumes on the flow is reduced as the density inversion parameter increases. Therefore, the flow is mainly driven by hot plumes, and the velocity magnitude and fluctuation decrease significantly.

The aim of this research is to understand the effect of the aspect ratio on the heat transfer ability and hydrodynamics characteristics of Rayleigh-Bénard convection of cold water near its maximum density in box-shaped containers. The Rayleigh number is fixed at 109, density inversion parameters are 0.3, 0.5 and 0.7, and the aspect ratio ranges from 1/60 to 1. Results indicate that the average Nusselt number presents a weak dependence on the aspect ratio at the large aspect ratio (A > 0.3). However, it reaches the maximum and then drops when the aspect ratio decreases from A = 0.3. Large scale circulations are observed for containers at the large aspect ratio, and the confinement of sidewalls weakens the large-scale circulation and eventually destructs it. At the large aspect ratio, the velocity fluctuation near the sidewalls is stronger than that in the center zone, because plumes primarily move along the sidewalls of the container. At a small aspect ratio, more plumes appear in the center of the container, where the fluctuation is stronger than that near sidewalls. The effect of cold plumes on the flow is reduced as the density inversion parameter increases. Therefore, the flow is mainly driven by hot plumes, and the velocity magnitude and fluctuation decrease significantly.

Categories: Latest papers in fluid mechanics

### Aerodynamic interaction of collective plates in side-by-side arrangement

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

In the tip-reversal upstroke of avian flight, individual feathers twist so as to create gaps between them. Although this behavior allows the feathers to function as individual lift-generating bodies, the lift generation mechanism of these multiple bodies remains unclear. This paper reports a numerical investigation of multiple stationary plates arranged side by side in a uniform flow. The aim is to elucidate the collective mechanism of the flow generated by the plates and the lift contribution of each plate. The angle of attack of each plate and the gap between the plates are varied to determine their influence on the flow and lift of the collection of plates. The time-averaged lift increases from the lowermost to the uppermost plate, and, at a high angle of attack, the total lift coefficient of the plates becomes greater than that of a single plate solely placed in a uniform flow. At a high angle of attack, vortex shedding from the upper plates is synchronized with some phase difference, resulting in synchronized lift fluctuations for individual plates and a reduction in the overall fluctuation amplitude. With an optimal gap ratio and angle of attack, the collective behavior of plates in side-by-side arrangement can be advantageous to enhance lift-generation performance.

In the tip-reversal upstroke of avian flight, individual feathers twist so as to create gaps between them. Although this behavior allows the feathers to function as individual lift-generating bodies, the lift generation mechanism of these multiple bodies remains unclear. This paper reports a numerical investigation of multiple stationary plates arranged side by side in a uniform flow. The aim is to elucidate the collective mechanism of the flow generated by the plates and the lift contribution of each plate. The angle of attack of each plate and the gap between the plates are varied to determine their influence on the flow and lift of the collection of plates. The time-averaged lift increases from the lowermost to the uppermost plate, and, at a high angle of attack, the total lift coefficient of the plates becomes greater than that of a single plate solely placed in a uniform flow. At a high angle of attack, vortex shedding from the upper plates is synchronized with some phase difference, resulting in synchronized lift fluctuations for individual plates and a reduction in the overall fluctuation amplitude. With an optimal gap ratio and angle of attack, the collective behavior of plates in side-by-side arrangement can be advantageous to enhance lift-generation performance.

Categories: Latest papers in fluid mechanics

### On the onset of convection in a highly permeable vertical porous layer with open boundaries

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

The unstable nature of buoyant flow in a vertical porous slab with a pure conduction temperature distribution is investigated. The permeable and isothermal boundaries are subject to a temperature difference, which is responsible for the basic stationary and parallel vertical flow in the slab. The momentum transfer is modeled by adopting the Darcy–Forchheimer law, thus including the quadratic form-drag contribution. The instability to small-amplitude perturbations is tested by parameterizing the basic stationary flow through the Darcy–Rayleigh number and the form-drag number. The modal analysis is carried out numerically with a pressure–temperature formulation of the governing equations for the perturbations. The neutral stability curves and the critical values of the wave number and of the Darcy–Rayleigh number are obtained for different prescribed values of the form-drag number.

The unstable nature of buoyant flow in a vertical porous slab with a pure conduction temperature distribution is investigated. The permeable and isothermal boundaries are subject to a temperature difference, which is responsible for the basic stationary and parallel vertical flow in the slab. The momentum transfer is modeled by adopting the Darcy–Forchheimer law, thus including the quadratic form-drag contribution. The instability to small-amplitude perturbations is tested by parameterizing the basic stationary flow through the Darcy–Rayleigh number and the form-drag number. The modal analysis is carried out numerically with a pressure–temperature formulation of the governing equations for the perturbations. The neutral stability curves and the critical values of the wave number and of the Darcy–Rayleigh number are obtained for different prescribed values of the form-drag number.

Categories: Latest papers in fluid mechanics

### The unification of disparate rheological measures in oscillatory shearing

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

Oscillatory shearing is a popular method to understand transient nonlinear rheology. Various viscoelastic metrics have been used to analyze oscillatory rheology with different perspectives. We present a translation between various viscoelastic metrics for oscillatory rheology, using the framework of sequence of physical processes (SPPs) as a basis. The relation between the SPP metrics and Fourier-based metrics, such as Fourier sine and cosine coefficients, and large and minimum strain and rate metrics is provided. The meaning of the curvature in elastic and viscous Lissajous figures is explained with the sign of the SPP viscoelastic metrics. A low dimensional interpretation of the SPP framework is presented, featuring the center, size, and orientation of a deltoid in a transient Cole-Cole plot. Finally, we show how statistical information regarding the amount of change exhibited by the SPP metrics over a period of oscillation can be used to enhance the presentation and understanding of traditionally performed amplitude sweep experiments.

Oscillatory shearing is a popular method to understand transient nonlinear rheology. Various viscoelastic metrics have been used to analyze oscillatory rheology with different perspectives. We present a translation between various viscoelastic metrics for oscillatory rheology, using the framework of sequence of physical processes (SPPs) as a basis. The relation between the SPP metrics and Fourier-based metrics, such as Fourier sine and cosine coefficients, and large and minimum strain and rate metrics is provided. The meaning of the curvature in elastic and viscous Lissajous figures is explained with the sign of the SPP viscoelastic metrics. A low dimensional interpretation of the SPP framework is presented, featuring the center, size, and orientation of a deltoid in a transient Cole-Cole plot. Finally, we show how statistical information regarding the amount of change exhibited by the SPP metrics over a period of oscillation can be used to enhance the presentation and understanding of traditionally performed amplitude sweep experiments.

Categories: Latest papers in fluid mechanics

### Inertial migration of circular particles in Poiseuille flow of a power-law fluid

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

The immersed boundary-lattice Boltzmann method is used to study the inertial migration of particles in Poiseuille flow of a power-law fluid. The effects of Reynolds number, power-law index, and blockage ratio on the formation of particle trains are explored. The results show that single particle with different initial positions reach the same equilibrium position for the same power-law index. The stable equilibrium position moves closer to the centerline under the higher power-law index and blockage ratio. One-line of eight particles distributed initially at a vertical position will migrate laterally to the vicinity of the wall and form single-line particle trains. The particle spacing is unstable and increases when particles migrate to the equilibrium position. The inertial focusing length is an important factor for analyzing the formation of particle trains, which will be longer with increasing the power-law index. The mean particle spacing will be reduced with increasing Re and blockage ratio. Two-lines of 12 particles distributed initially and abreast along both sides of the centerline will migrate to the vicinity of the wall and form staggered particle trains. Due to the multiparticles interaction, the final particle equilibrium position will deviate from the single particle equilibrium position. The axial spacing between two neighboring particles is stable or fluctuates within a certain range. The particle spacing decreases with increasing the power-law index and blockage ratio, and with decreasing Re. The shear-thinning fluid is beneficial to the formation of single-line particle trains and staggered particle trains.

The immersed boundary-lattice Boltzmann method is used to study the inertial migration of particles in Poiseuille flow of a power-law fluid. The effects of Reynolds number, power-law index, and blockage ratio on the formation of particle trains are explored. The results show that single particle with different initial positions reach the same equilibrium position for the same power-law index. The stable equilibrium position moves closer to the centerline under the higher power-law index and blockage ratio. One-line of eight particles distributed initially at a vertical position will migrate laterally to the vicinity of the wall and form single-line particle trains. The particle spacing is unstable and increases when particles migrate to the equilibrium position. The inertial focusing length is an important factor for analyzing the formation of particle trains, which will be longer with increasing the power-law index. The mean particle spacing will be reduced with increasing Re and blockage ratio. Two-lines of 12 particles distributed initially and abreast along both sides of the centerline will migrate to the vicinity of the wall and form staggered particle trains. Due to the multiparticles interaction, the final particle equilibrium position will deviate from the single particle equilibrium position. The axial spacing between two neighboring particles is stable or fluctuates within a certain range. The particle spacing decreases with increasing the power-law index and blockage ratio, and with decreasing Re. The shear-thinning fluid is beneficial to the formation of single-line particle trains and staggered particle trains.

Categories: Latest papers in fluid mechanics

### Particle-laden thin-film flow in helical channels with arbitrary shallow cross-sectional shape

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

Particle-laden flows in helical channels are of interest for their applications in spiral particle separators used in the mining and mineral processing industries. In this paper, we extend the previous work of Lee, Stokes, and Bertozzi [“Behaviour of a particle-laden flow in a spiral channel,” Phys. Fluids 26, 043302 (2014)] by studying thin-film flows of monodisperse particle-laden fluid in helically wound channels of arbitrary centerline curvature and torsion and arbitrary cross-sectional shape. In the case where the particles are uniformly distributed through the depth of the film, significant analytic progress can be made yielding insight into the influence of channel geometry on particle distribution across the channel cross section: the governing equations reduce to a single nonlinear ordinary differential equation, which is readily integrated numerically to obtain the solution subject to appropriate boundary conditions. Motivated by possible application to the design of spiral separators, we consider the effects of changing the channel centerline geometry, the cross-sectional shape and the particle density on the resulting flows, and the radial distribution of particles. Our results support the findings in the work of Arnold, Stokes, and Green [“Thin-film flow in helically wound rectangular channels of arbitrary torsion and curvature,” J. Fluid Mech. 764, 76–94 (2015)] regarding the effect of channel centerline geometry and cross-sectional shape on flows in particle-free regions. In particle-rich regions, similar effects are seen although the primary velocity is lower due to increased effective mixture viscosity. Of key interest is the effect of channel geometry on the focusing of the particles for given fluxes of fluid and particles. We find that introducing a trench into the channel cross section, a feature often used in commercial spiral particle separators, leads to a smaller radial width of the particle-rich region, i.e., sharper focusing of the particles, which is consistent with experiments showing that channel geometry influences particle separation in a spiral separator.

Particle-laden flows in helical channels are of interest for their applications in spiral particle separators used in the mining and mineral processing industries. In this paper, we extend the previous work of Lee, Stokes, and Bertozzi [“Behaviour of a particle-laden flow in a spiral channel,” Phys. Fluids 26, 043302 (2014)] by studying thin-film flows of monodisperse particle-laden fluid in helically wound channels of arbitrary centerline curvature and torsion and arbitrary cross-sectional shape. In the case where the particles are uniformly distributed through the depth of the film, significant analytic progress can be made yielding insight into the influence of channel geometry on particle distribution across the channel cross section: the governing equations reduce to a single nonlinear ordinary differential equation, which is readily integrated numerically to obtain the solution subject to appropriate boundary conditions. Motivated by possible application to the design of spiral separators, we consider the effects of changing the channel centerline geometry, the cross-sectional shape and the particle density on the resulting flows, and the radial distribution of particles. Our results support the findings in the work of Arnold, Stokes, and Green [“Thin-film flow in helically wound rectangular channels of arbitrary torsion and curvature,” J. Fluid Mech. 764, 76–94 (2015)] regarding the effect of channel centerline geometry and cross-sectional shape on flows in particle-free regions. In particle-rich regions, similar effects are seen although the primary velocity is lower due to increased effective mixture viscosity. Of key interest is the effect of channel geometry on the focusing of the particles for given fluxes of fluid and particles. We find that introducing a trench into the channel cross section, a feature often used in commercial spiral particle separators, leads to a smaller radial width of the particle-rich region, i.e., sharper focusing of the particles, which is consistent with experiments showing that channel geometry influences particle separation in a spiral separator.

Categories: Latest papers in fluid mechanics

### Mechanism of end-gas autoignition induced by flame-pressure interactions in confined space

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

The main objective of this work is to comprehensively provide a fundamental understanding of the entire process of the flame-pressure wave interactions with end-gas autoignition and detonation development in a confined chamber by two-dimensional numerical simulations with a stoichiometric hydrogen/air mixture. The flame dynamics, pressure wave propagation, and its structure evolution, together with the mechanism of autoignition and detonation development in the end gas, are analyzed in detail. Six stages, including spherical flame, finger flame, flame with its skirt touching the sidewalls, flame-pressure wave interactions, end-gas autoignition induced by the flame-pressure wave interactions, and detonation development, are observed for the flame development in the confined space. The results demonstrate that the flame-pressure wave multi-interactions result in violent oscillations of the flame shape and speed. Three stages of flame shape evolution during each interaction, backward propagation of the flame front, stretch of the flame front at the boundary layer, and formation of the tulip flame, are captured. A new mechanism in terms of combined effects of the viscous boundary layer and pressure waves is provided for the formation of the tulip flame. It is also found that the velocity distributions in the boundary layer show the trend of increase first and then decrease after the pressure waves pass the fields twice in the opposite directions. The autoignition occurrence and detonation initiation at different positions and different moments in the end-gas region are analyzed. It is indicated that the nonuniform temperature distribution induced by the reflections of pressure waves and the specific pressure wave structures can be responsible for this phenomenon.

The main objective of this work is to comprehensively provide a fundamental understanding of the entire process of the flame-pressure wave interactions with end-gas autoignition and detonation development in a confined chamber by two-dimensional numerical simulations with a stoichiometric hydrogen/air mixture. The flame dynamics, pressure wave propagation, and its structure evolution, together with the mechanism of autoignition and detonation development in the end gas, are analyzed in detail. Six stages, including spherical flame, finger flame, flame with its skirt touching the sidewalls, flame-pressure wave interactions, end-gas autoignition induced by the flame-pressure wave interactions, and detonation development, are observed for the flame development in the confined space. The results demonstrate that the flame-pressure wave multi-interactions result in violent oscillations of the flame shape and speed. Three stages of flame shape evolution during each interaction, backward propagation of the flame front, stretch of the flame front at the boundary layer, and formation of the tulip flame, are captured. A new mechanism in terms of combined effects of the viscous boundary layer and pressure waves is provided for the formation of the tulip flame. It is also found that the velocity distributions in the boundary layer show the trend of increase first and then decrease after the pressure waves pass the fields twice in the opposite directions. The autoignition occurrence and detonation initiation at different positions and different moments in the end-gas region are analyzed. It is indicated that the nonuniform temperature distribution induced by the reflections of pressure waves and the specific pressure wave structures can be responsible for this phenomenon.

Categories: Latest papers in fluid mechanics

### Stream broadening due to fluid shear across the wider transverse dimension of a free-flow zone electrophoresis channel

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

While the pressure-gradient applied along the length of a free-flow zone electrophoresis (FFZE) chamber is known to produce a parabolic flow profile for the carrier electrolyte across the narrower channel dimension (typically the channel depth), additional fluid shear can arise across the channel width due to a variety of reasons. Most commonly, any variation in the pressure-drop or channel depth across this wider dimension can lead to a gradient in the liquid flow velocity along it, significantly altering the stream broadening and, thereby, the separation performance of the assay. This article assesses the effect of such fluid shear on stream broadening during the FFZE process by describing a mathematical framework for solving the relevant advection-diffusion equation based on the method-of-moments approach. A closed-form expression for the leading order term describing the additional contribution to the spatial stream variance has been derived considering a small linear gradient in the liquid velocity across the wider transverse dimension of the FFZE chamber. The noted analysis predicts this contribution to be governed by two Péclet numbers that are evaluated based on the axial pressure-driven flow and transverse electrophoretic solute velocities. More importantly, this contribution is shown to vary quadratically with the axial distance traversed by the analyte stream as opposed to the classical linear variation known for all other stream broadening contributions in FFZE systems. The results from the analytic theory have been validated with Monte Carlo simulations, which also establish a time and length scale over which the noted analytical results are applicable.

While the pressure-gradient applied along the length of a free-flow zone electrophoresis (FFZE) chamber is known to produce a parabolic flow profile for the carrier electrolyte across the narrower channel dimension (typically the channel depth), additional fluid shear can arise across the channel width due to a variety of reasons. Most commonly, any variation in the pressure-drop or channel depth across this wider dimension can lead to a gradient in the liquid flow velocity along it, significantly altering the stream broadening and, thereby, the separation performance of the assay. This article assesses the effect of such fluid shear on stream broadening during the FFZE process by describing a mathematical framework for solving the relevant advection-diffusion equation based on the method-of-moments approach. A closed-form expression for the leading order term describing the additional contribution to the spatial stream variance has been derived considering a small linear gradient in the liquid velocity across the wider transverse dimension of the FFZE chamber. The noted analysis predicts this contribution to be governed by two Péclet numbers that are evaluated based on the axial pressure-driven flow and transverse electrophoretic solute velocities. More importantly, this contribution is shown to vary quadratically with the axial distance traversed by the analyte stream as opposed to the classical linear variation known for all other stream broadening contributions in FFZE systems. The results from the analytic theory have been validated with Monte Carlo simulations, which also establish a time and length scale over which the noted analytical results are applicable.

Categories: Latest papers in fluid mechanics

### Trapping of metallic nanoparticles under the free surface of superfluid helium in a static electric field

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

Electrically charged metallic microparticles and nanoparticles have been trapped under a free surface of superfluid 4He in a vertical static electric field. We report the details of the trapping technique and the observed dynamics of the trapped particles moving along the surface and driven by surface waves, by a static horizontal electric field, and by a thermal counterflow within the surface layer of liquid He.

Electrically charged metallic microparticles and nanoparticles have been trapped under a free surface of superfluid 4He in a vertical static electric field. We report the details of the trapping technique and the observed dynamics of the trapped particles moving along the surface and driven by surface waves, by a static horizontal electric field, and by a thermal counterflow within the surface layer of liquid He.

Categories: Latest papers in fluid mechanics

### The age of a wake

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

This study attempts to quantify the decay rates of stratified wakes in active oceanic environments, characterized by the presence of intermittent turbulence and double-diffusive convection. Of particular interest is the possibility of utilizing standard oceanographic microstructure measurements as a means of wake identification and analysis. The investigation is based on a series of direct numerical simulations of wakes produced by a sphere uniformly propagating in stratified two-component fluids. We examine and compare the evolution of wakes in fluid systems that are (i) initially quiescent, (ii) double-diffusively unstable, and (iii) contain preexisting turbulence. The model diagnostics are focused primarily on the dissipation of turbulent kinetic energy (ε) and thermal variance (χ). The analysis of decay patterns of ε and χ indicates that microstructure generated by an object of D = 0.6 m in diameter moving at the speed of U = 0.02 m/s could be detected, using modern high-resolution profiling instruments, for 0.5–0.7 h. The detection period depends on environmental conditions; convective overturns are shown to be particularly effective in terms of dispersion of microscale wake signatures. The extrapolation of model results to objects of ∼10 m in diameter propagating with speeds of ∼10 m/s suggests that the microstructure-based wake detection is feasible for at least 4 h after the object’s passage through the monitored areas. The overall conclusion from our study is that the measurement of microscale signatures of turbulent wakes could represent a viable method for hydrodynamic detection of propagating submersibles.

This study attempts to quantify the decay rates of stratified wakes in active oceanic environments, characterized by the presence of intermittent turbulence and double-diffusive convection. Of particular interest is the possibility of utilizing standard oceanographic microstructure measurements as a means of wake identification and analysis. The investigation is based on a series of direct numerical simulations of wakes produced by a sphere uniformly propagating in stratified two-component fluids. We examine and compare the evolution of wakes in fluid systems that are (i) initially quiescent, (ii) double-diffusively unstable, and (iii) contain preexisting turbulence. The model diagnostics are focused primarily on the dissipation of turbulent kinetic energy (ε) and thermal variance (χ). The analysis of decay patterns of ε and χ indicates that microstructure generated by an object of D = 0.6 m in diameter moving at the speed of U = 0.02 m/s could be detected, using modern high-resolution profiling instruments, for 0.5–0.7 h. The detection period depends on environmental conditions; convective overturns are shown to be particularly effective in terms of dispersion of microscale wake signatures. The extrapolation of model results to objects of ∼10 m in diameter propagating with speeds of ∼10 m/s suggests that the microstructure-based wake detection is feasible for at least 4 h after the object’s passage through the monitored areas. The overall conclusion from our study is that the measurement of microscale signatures of turbulent wakes could represent a viable method for hydrodynamic detection of propagating submersibles.

Categories: Latest papers in fluid mechanics

### Effect of vortex-induced vibration of finned cylinders on heat transfer enhancement

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

Two-degree-of-freedom vortex-induced vibration (VIV) of a finned cylinder with heat transfer is studied numerically at the Reynolds number Re = 150. The governing equations in the Arbitrary Lagrangian-Eulerian frame are solved by the finite volume method. The dynamics of the oscillating cylinder (with or without fins) in the fluid flow was approximated as a mass-spring system. The effects of the number and arrangement of the fins (14 different cases) on the vortex shedding pattern, vibration amplitude, and frequency and heat transfer of the cylinder are investigated and discussed. The results indicate that in comparison with the stationary state, the effects of the number and arrangement of the fins on the wake pattern and the heat transfer enhancement in the VIV state are significant. Different vortex shedding pattern like 2S, P, 2P, S + P and combination of them with stable or unstable interactions between vortices and cylinders are observed in an oscillating cylinder. In the vibration state of finned cylinders, the heat transfer enhances up to 50.4% with respect to the stationary state and increases up to 64% with respect to the stationary smooth cylinder.

Two-degree-of-freedom vortex-induced vibration (VIV) of a finned cylinder with heat transfer is studied numerically at the Reynolds number Re = 150. The governing equations in the Arbitrary Lagrangian-Eulerian frame are solved by the finite volume method. The dynamics of the oscillating cylinder (with or without fins) in the fluid flow was approximated as a mass-spring system. The effects of the number and arrangement of the fins (14 different cases) on the vortex shedding pattern, vibration amplitude, and frequency and heat transfer of the cylinder are investigated and discussed. The results indicate that in comparison with the stationary state, the effects of the number and arrangement of the fins on the wake pattern and the heat transfer enhancement in the VIV state are significant. Different vortex shedding pattern like 2S, P, 2P, S + P and combination of them with stable or unstable interactions between vortices and cylinders are observed in an oscillating cylinder. In the vibration state of finned cylinders, the heat transfer enhances up to 50.4% with respect to the stationary state and increases up to 64% with respect to the stationary smooth cylinder.

Categories: Latest papers in fluid mechanics

### Numerical investigation of wake structures of an atmospheric entry capsule by modal analysis

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

This study investigates the flow structures behind an atmospheric entry capsule at Mach number 0.4 through an improved detached eddy simulation and a modal analysis. The simulated flowfields reveal relatively low-frequency peaks of St ≈ 0.016 and St = 0.17–0.2 in the aerodynamic coefficient variation, where St is the nondimensional frequency. Then, the dominant fluid structures that cause the frequency peaks are identified through dynamic mode decomposition and the compressive-sensing-based mode selection method. Many of the dominant fluid phenomena have a frequency of St ≈ 0.2. In this frequency range, the fluid phenomena are mainly characterized with a large-scale vortex shedding separated from the capsule’s shoulder part and with a helical fluid structure in the wake. Moreover, the variation in the lift coefficient of the capsule is mainly attributed to the large-scale vortex shedding phenomenon. Furthermore, a fluid phenomenon at a frequency of St = O(0.01) is found, which describes the pulsation, or periodic growth or shrinkage, of the recirculation bubble, accompanied by pressure fluctuation behind the capsule that exerts a large drag fluctuation of the capsule. Additionally, this phenomenon seems related to the dynamic instability phenomena of the capsule, as indicated by its time scale, which is close to that of the capsule’s attitude motion.

This study investigates the flow structures behind an atmospheric entry capsule at Mach number 0.4 through an improved detached eddy simulation and a modal analysis. The simulated flowfields reveal relatively low-frequency peaks of St ≈ 0.016 and St = 0.17–0.2 in the aerodynamic coefficient variation, where St is the nondimensional frequency. Then, the dominant fluid structures that cause the frequency peaks are identified through dynamic mode decomposition and the compressive-sensing-based mode selection method. Many of the dominant fluid phenomena have a frequency of St ≈ 0.2. In this frequency range, the fluid phenomena are mainly characterized with a large-scale vortex shedding separated from the capsule’s shoulder part and with a helical fluid structure in the wake. Moreover, the variation in the lift coefficient of the capsule is mainly attributed to the large-scale vortex shedding phenomenon. Furthermore, a fluid phenomenon at a frequency of St = O(0.01) is found, which describes the pulsation, or periodic growth or shrinkage, of the recirculation bubble, accompanied by pressure fluctuation behind the capsule that exerts a large drag fluctuation of the capsule. Additionally, this phenomenon seems related to the dynamic instability phenomena of the capsule, as indicated by its time scale, which is close to that of the capsule’s attitude motion.

Categories: Latest papers in fluid mechanics