# Physics of Fluids

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

*Updated:*2 days 19 hours ago

### Three-dimensional vortical structures generated by plasma synthetic jets in crossflow

Physics of Fluids, Volume 32, Issue 6, June 2020.

In the present study, phase-locked tomographic particle image velocimetry measurements are performed to obtain the complex three-dimensional vortex system created by the interaction of plasma synthetic jets with external crossflow. Three orifice configurations (round, transverse slot, and longitudinal slot) are investigated. For the round orifice case, the vortex system consists of a starting vortex ring surrounding the jet head, a hanging vortex pair residing in the two lateral sides of the jet body, several shear layer vortices bridging the two legs of the hanging vortex pair, and a hairpin vortex induced by the low-speed secondary jet. For the slot orifice cases, the above vortex system is also present; nevertheless, the interconnections of the vortices are further intersected by the rib vortices that are branched out of the elongated vortex ring during axis switching. The counter-rotating vortex pair observed in the far field is essentially evolving from the hanging vortex pair in the near field.

In the present study, phase-locked tomographic particle image velocimetry measurements are performed to obtain the complex three-dimensional vortex system created by the interaction of plasma synthetic jets with external crossflow. Three orifice configurations (round, transverse slot, and longitudinal slot) are investigated. For the round orifice case, the vortex system consists of a starting vortex ring surrounding the jet head, a hanging vortex pair residing in the two lateral sides of the jet body, several shear layer vortices bridging the two legs of the hanging vortex pair, and a hairpin vortex induced by the low-speed secondary jet. For the slot orifice cases, the above vortex system is also present; nevertheless, the interconnections of the vortices are further intersected by the rib vortices that are branched out of the elongated vortex ring during axis switching. The counter-rotating vortex pair observed in the far field is essentially evolving from the hanging vortex pair in the near field.

Categories: Latest papers in fluid mechanics

### Fluvial instabilities

Physics of Fluids, Volume 32, Issue 6, June 2020.

Fluvial instabilities originate from an interplay between the carrier fluid and the erodible loose boundary at their interface, manifesting a variety of sedimentary architectures with length scales spanning from a few millimeters to hundreds of meters. This review sheds light on the current state-of-the-science of the subject, explaining the fluvial instabilities from three broad perspectives. They are micro-scale, meso-scale, and macro-scale instabilities. The interactions between the near-bed hydrodynamics and the sediment dynamics in generating various kinds of instabilities, including their natures and driving mechanisms, are thoroughly appraised in the light of laboratory experimental results, field observations, and theoretical backgrounds. Besides, this review addresses the current challenges, delineating key points as a future research scope.

Fluvial instabilities originate from an interplay between the carrier fluid and the erodible loose boundary at their interface, manifesting a variety of sedimentary architectures with length scales spanning from a few millimeters to hundreds of meters. This review sheds light on the current state-of-the-science of the subject, explaining the fluvial instabilities from three broad perspectives. They are micro-scale, meso-scale, and macro-scale instabilities. The interactions between the near-bed hydrodynamics and the sediment dynamics in generating various kinds of instabilities, including their natures and driving mechanisms, are thoroughly appraised in the light of laboratory experimental results, field observations, and theoretical backgrounds. Besides, this review addresses the current challenges, delineating key points as a future research scope.

Categories: Latest papers in fluid mechanics

### Improving the k–[math]–[math]–Ar transition model by the field inversion and machine learning framework

Physics of Fluids, Volume 32, Issue 6, June 2020.

Accurate simulation of transition from the laminar to the turbulent flow is of great importance in industrial applications. In the present work, the framework of field inversion and machine learning has been applied to improve the four-equation k–ω–γ–Ar transition model. The low-speed transitional flows past two airfoils were numerically simulated. Based on the experimental transition locations, the regularizing ensemble Kalman filtering (EnKF) was performed to obtain the distributions of space-varied correction terms for the first mode time scale in the transitional flows over a natural-laminar-flow (NLF) airfoil, NLF(1)-0416. Then, two machine learning methods, random forest (RF) and artificial neutral network (NN), were adopted to construct the mapping from the mean flow variables to the correction terms. Finally, the learned models were embedded into the original solver. The results show that the regularizing EnKF can efficiently obtain the posterior distribution of the correction terms only by the transition locations. Meanwhile, both the RF- and NN-augmented transition models can predict more accurate transition locations past NLF(1)-0416 at both interpolated and extrapolated angles of attack. Moreover, the RF-augmented model can predict more accurate transitional flows on both the windward and leeward sides of NACA0012 at the same angle of attack. It indicates that the discrepancies within the model are learned and reduced. The modified model has good applicability and generalization ability. Furthermore, by analyzing the relative importance of the features in the RF model, it is found that the streamwise pressure gradient plays the most important role in the physical information and interpretation of the learned model.

Accurate simulation of transition from the laminar to the turbulent flow is of great importance in industrial applications. In the present work, the framework of field inversion and machine learning has been applied to improve the four-equation k–ω–γ–Ar transition model. The low-speed transitional flows past two airfoils were numerically simulated. Based on the experimental transition locations, the regularizing ensemble Kalman filtering (EnKF) was performed to obtain the distributions of space-varied correction terms for the first mode time scale in the transitional flows over a natural-laminar-flow (NLF) airfoil, NLF(1)-0416. Then, two machine learning methods, random forest (RF) and artificial neutral network (NN), were adopted to construct the mapping from the mean flow variables to the correction terms. Finally, the learned models were embedded into the original solver. The results show that the regularizing EnKF can efficiently obtain the posterior distribution of the correction terms only by the transition locations. Meanwhile, both the RF- and NN-augmented transition models can predict more accurate transition locations past NLF(1)-0416 at both interpolated and extrapolated angles of attack. Moreover, the RF-augmented model can predict more accurate transitional flows on both the windward and leeward sides of NACA0012 at the same angle of attack. It indicates that the discrepancies within the model are learned and reduced. The modified model has good applicability and generalization ability. Furthermore, by analyzing the relative importance of the features in the RF model, it is found that the streamwise pressure gradient plays the most important role in the physical information and interpretation of the learned model.

Categories: Latest papers in fluid mechanics

### Moist-convective thermal rotating shallow water model

Physics of Fluids, Volume 32, Issue 6, June 2020.

We show how the moist-convective rotating shallow water model, where the moist convection and the related latent heat release are incorporated into the standard rotating shallow water model of the atmosphere, can be improved by introducing, in a self-consistent way, horizontal gradients of potential temperature and changes of the latter due to the condensation heating, radiative cooling, and ocean-atmosphere heat fluxes. We also construct the quasi-geostrophic limit of the model in mid-latitudes and its weak-gradient limits in the equatorial region. The capabilities of the new model are illustrated by the examples of convection-coupled gravity waves and equatorial waves produced by the relaxation of localized pressure and potential temperature anomalies in the presence of moist convection.

We show how the moist-convective rotating shallow water model, where the moist convection and the related latent heat release are incorporated into the standard rotating shallow water model of the atmosphere, can be improved by introducing, in a self-consistent way, horizontal gradients of potential temperature and changes of the latter due to the condensation heating, radiative cooling, and ocean-atmosphere heat fluxes. We also construct the quasi-geostrophic limit of the model in mid-latitudes and its weak-gradient limits in the equatorial region. The capabilities of the new model are illustrated by the examples of convection-coupled gravity waves and equatorial waves produced by the relaxation of localized pressure and potential temperature anomalies in the presence of moist convection.

Categories: Latest papers in fluid mechanics

### A computational fluid dynamics approach for full characterization of muffler without and with exhaust flow

Physics of Fluids, Volume 32, Issue 6, June 2020.

Compared to the linear frequency domain method, the transient Computational Fluid Dynamics (CFD) method is more effective when analyzing the effect of complex flow in the muffler on its acoustic characteristics. However, most of the existing CFD methods focus on the calculation of the transmission loss (TL) for the muffler only. The other evaluation parameters, such as noise reduction (NR), are rarely investigated. In this paper, a CFD approach was developed systematically for charactering TL, NR, and transfer matrix (TM) of the muffler in the cases without and with exhaust flow. In the proposed approach, only one mesh model with a correction pipe is needed based on two simulation runs. The non-reflective boundary was used as the termination of the correction pipe in the calculation for the TL, while the reflective pressure boundary was set on the correction pipe end in the calculation for the NR. The TM was then derived from the time-domain pressure and mass velocity obtained in the previous runs for calculating TL and NR. The proposed CFD approach was applied to two simple expansion chambers, and the computational predictions of TL, NR, and TM were validated successfully both with the measured results and the analytical results. In conclusion, the proposed CFD approach is effective for full characterization (TL, NR, and TM) of exhaust mufflers without and with exhaust flow.

Compared to the linear frequency domain method, the transient Computational Fluid Dynamics (CFD) method is more effective when analyzing the effect of complex flow in the muffler on its acoustic characteristics. However, most of the existing CFD methods focus on the calculation of the transmission loss (TL) for the muffler only. The other evaluation parameters, such as noise reduction (NR), are rarely investigated. In this paper, a CFD approach was developed systematically for charactering TL, NR, and transfer matrix (TM) of the muffler in the cases without and with exhaust flow. In the proposed approach, only one mesh model with a correction pipe is needed based on two simulation runs. The non-reflective boundary was used as the termination of the correction pipe in the calculation for the TL, while the reflective pressure boundary was set on the correction pipe end in the calculation for the NR. The TM was then derived from the time-domain pressure and mass velocity obtained in the previous runs for calculating TL and NR. The proposed CFD approach was applied to two simple expansion chambers, and the computational predictions of TL, NR, and TM were validated successfully both with the measured results and the analytical results. In conclusion, the proposed CFD approach is effective for full characterization (TL, NR, and TM) of exhaust mufflers without and with exhaust flow.

Categories: Latest papers in fluid mechanics

### An efficient selective cell-based smoothed finite element approach to fluid-structure interaction

Physics of Fluids, Volume 32, Issue 6, June 2020.

This paper describes an efficient and simple selective cell-based smoothed finite element method (CS-FEM) for partitioned fluid–structure interaction. Depending on a fractional-step fluid solver, a selective smoothed integration scheme is proposed for the Navier–Stokes equations in stationary and deforming domains. A simple hourglass stabilization is then introduced into the under-integrated smoothed Galerkin weak form of the fractional-step algorithm. As a result, the computational efficiency is considerably boosted in comparison with existing CS-FEM formulation. Meanwhile, the CS-FEM is applied to spatially discretize the elastodynamics equations of nonlinear solids as usual. After discussing the mesh moving strategy, the gradient smoothing is performed in each individual interface element to evaluate the fluid forces acting on oscillating rigid and flexible bodies. The block Gauss–Seidel procedure is employed to couple all interacting fields under the arbitrary Lagrangian–Eulerian description. Several numerical examples are presented to demonstrate the desirable efficiency and accuracy of the proposed methodology.

This paper describes an efficient and simple selective cell-based smoothed finite element method (CS-FEM) for partitioned fluid–structure interaction. Depending on a fractional-step fluid solver, a selective smoothed integration scheme is proposed for the Navier–Stokes equations in stationary and deforming domains. A simple hourglass stabilization is then introduced into the under-integrated smoothed Galerkin weak form of the fractional-step algorithm. As a result, the computational efficiency is considerably boosted in comparison with existing CS-FEM formulation. Meanwhile, the CS-FEM is applied to spatially discretize the elastodynamics equations of nonlinear solids as usual. After discussing the mesh moving strategy, the gradient smoothing is performed in each individual interface element to evaluate the fluid forces acting on oscillating rigid and flexible bodies. The block Gauss–Seidel procedure is employed to couple all interacting fields under the arbitrary Lagrangian–Eulerian description. Several numerical examples are presented to demonstrate the desirable efficiency and accuracy of the proposed methodology.

Categories: Latest papers in fluid mechanics

### Dynamics of the passive pulsation of a surface-attached air bubble subjected to a nearby oscillating spark-generated bubble

Physics of Fluids, Volume 32, Issue 6, June 2020.

The dynamics of a spark-generated bubble (a discharge short circuit) generated in proximity to a stationary air bubble attached to a plate is experimentally investigated by high-speed photography. Numerous interesting and complex interactions occur during the two bubble coupling pulsation owing to the deformation properties or “free surface” characteristics supplied to the plate by the attached air bubble. Complex bubble jetting behaviors, such as bubble splitting, jets away from the plate, variable directional jets, and multidirectional jets are observed. Passive pulsation of the air bubble is observed in response to the spark bubble. Moreover, five types of bubble behaviors are summarized: bubble coalescence, the air bubble skirt phenomenon, the “mountain”-shaped bubble, and the “cup cover”-shaped air bubble with or without splitting. To develop a better understanding of the coupling interactions between the two bubbles during their oscillations, four types of bubble volume–time curves are summarized using the image outline identification code established to obtain information regarding the bubble shape. The complex phenomena during the two-bubble interactions, such as the bubble jetting direction, air bubble shapes, and volume–time curves, are summarized as graphs and are highly dependent on the bubble size ratio, dimensionless cavitation bubble oscillation time, and initial displacement parameter.

The dynamics of a spark-generated bubble (a discharge short circuit) generated in proximity to a stationary air bubble attached to a plate is experimentally investigated by high-speed photography. Numerous interesting and complex interactions occur during the two bubble coupling pulsation owing to the deformation properties or “free surface” characteristics supplied to the plate by the attached air bubble. Complex bubble jetting behaviors, such as bubble splitting, jets away from the plate, variable directional jets, and multidirectional jets are observed. Passive pulsation of the air bubble is observed in response to the spark bubble. Moreover, five types of bubble behaviors are summarized: bubble coalescence, the air bubble skirt phenomenon, the “mountain”-shaped bubble, and the “cup cover”-shaped air bubble with or without splitting. To develop a better understanding of the coupling interactions between the two bubbles during their oscillations, four types of bubble volume–time curves are summarized using the image outline identification code established to obtain information regarding the bubble shape. The complex phenomena during the two-bubble interactions, such as the bubble jetting direction, air bubble shapes, and volume–time curves, are summarized as graphs and are highly dependent on the bubble size ratio, dimensionless cavitation bubble oscillation time, and initial displacement parameter.

Categories: Latest papers in fluid mechanics

### Oblique elastic plate impact on thin liquid layer

Physics of Fluids, Volume 32, Issue 6, June 2020.

The present study is concerned with possible mechanisms of air entrainment in a thin liquid layer caused by oblique impact of a deformable body on the layer. The two-dimensional unsteady problem of oblique elastic plate impact is considered within the thin-layer approximation for the first time. The plate deflection is described by the Euler beam equation. The plate edges are free of stresses and shear forces. The plate deflections are comparable with the liquid layer thickness. It is revealed in this paper that, for a stiff plate, the initial impact by the trailing edge makes the plate rotate with the leading plate edge entering water before the wetted part of the plate arrives at this edge. The air cavity trapped in such cases can be as long as 40% of the plate length. For a flexible plate, the impact does not cause the plate rotation. However, the dry part of the plate in front of the advancing wetted region is deflected toward the liquid layer also trapping the air. The numerical results are presented for elastic and rigid motions of the plate, hydrodynamic pressure in the wetted part of the plate, position of this wetted part, and the flow beneath the plate.

The present study is concerned with possible mechanisms of air entrainment in a thin liquid layer caused by oblique impact of a deformable body on the layer. The two-dimensional unsteady problem of oblique elastic plate impact is considered within the thin-layer approximation for the first time. The plate deflection is described by the Euler beam equation. The plate edges are free of stresses and shear forces. The plate deflections are comparable with the liquid layer thickness. It is revealed in this paper that, for a stiff plate, the initial impact by the trailing edge makes the plate rotate with the leading plate edge entering water before the wetted part of the plate arrives at this edge. The air cavity trapped in such cases can be as long as 40% of the plate length. For a flexible plate, the impact does not cause the plate rotation. However, the dry part of the plate in front of the advancing wetted region is deflected toward the liquid layer also trapping the air. The numerical results are presented for elastic and rigid motions of the plate, hydrodynamic pressure in the wetted part of the plate, position of this wetted part, and the flow beneath the plate.

Categories: Latest papers in fluid mechanics

### Droplet dynamics on viscoelastic soft substrate: Toward coalescence control

Physics of Fluids, Volume 32, Issue 6, June 2020.

We study the dynamical behavior of droplets on a viscoelastic soft substrate. Using thin film approximation for the hydrodynamics and time-dependent Winkler’s substrate model, we show numerically how droplet growth depends strongly on the viscous damping characteristic of the substrate, leading to asymmetric stick-slip dynamics corroborated by experimental observations. Scaling arguments are presented to rationalize radial growth and the underlying substrate response to viscoelastic limits. Using an adjacent pair of inflating droplets, we report strongly diverse coalescence outcomes with non-linear coalescence times, including attraction, repulsion, and remarkably, a separation regime, within which the two droplets grow away from each other and remain separated due to intervening wetting ridges. Together, our results indicate strong interactions between the substrate and the droplet across viscoelastic and capillary timescales, with practical implications for smart surface engineering, condensation, and coalescence control.

We study the dynamical behavior of droplets on a viscoelastic soft substrate. Using thin film approximation for the hydrodynamics and time-dependent Winkler’s substrate model, we show numerically how droplet growth depends strongly on the viscous damping characteristic of the substrate, leading to asymmetric stick-slip dynamics corroborated by experimental observations. Scaling arguments are presented to rationalize radial growth and the underlying substrate response to viscoelastic limits. Using an adjacent pair of inflating droplets, we report strongly diverse coalescence outcomes with non-linear coalescence times, including attraction, repulsion, and remarkably, a separation regime, within which the two droplets grow away from each other and remain separated due to intervening wetting ridges. Together, our results indicate strong interactions between the substrate and the droplet across viscoelastic and capillary timescales, with practical implications for smart surface engineering, condensation, and coalescence control.

Categories: Latest papers in fluid mechanics

### Exploration and prediction of fluid dynamical systems using auto-encoder technology

Physics of Fluids, Volume 32, Issue 6, June 2020.

Machine-learning (ML) algorithms offer a new path for investigating high-dimensional, nonlinear problems, such as flow-dynamical systems. The development of ML methods, associated with the abundance of data and combined with fluid-dynamics knowledge, offers a unique opportunity for achieving significant breakthroughs in terms of advances in flow prediction and its control. The objective of this paper is to discuss some possibilities offered by ML algorithms for exploring and predicting flow-dynamical systems. First, an overview of basic concepts underpinning artificial neural networks, deep neural networks, and convolutional neural networks is given. Building upon this overview, the concept of Auto-Encoders (AEs) is introduced. An AE constitutes an unsupervised learning technique in which a neural-network architecture is leveraged for determining a data structure that results from reducing the dimensionality of the native system. For the particular test case of flow behind a cylinder, it is shown that combinations of an AE with other ML algorithms can be used (i) to provide a low-dimensional dynamical model (a probabilistic flow prediction), (ii) to give a deterministic flow prediction, and (iii) to retrieve high-resolution data in the spatio-temporal domain from contaminated and/or under-sampled data.

Machine-learning (ML) algorithms offer a new path for investigating high-dimensional, nonlinear problems, such as flow-dynamical systems. The development of ML methods, associated with the abundance of data and combined with fluid-dynamics knowledge, offers a unique opportunity for achieving significant breakthroughs in terms of advances in flow prediction and its control. The objective of this paper is to discuss some possibilities offered by ML algorithms for exploring and predicting flow-dynamical systems. First, an overview of basic concepts underpinning artificial neural networks, deep neural networks, and convolutional neural networks is given. Building upon this overview, the concept of Auto-Encoders (AEs) is introduced. An AE constitutes an unsupervised learning technique in which a neural-network architecture is leveraged for determining a data structure that results from reducing the dimensionality of the native system. For the particular test case of flow behind a cylinder, it is shown that combinations of an AE with other ML algorithms can be used (i) to provide a low-dimensional dynamical model (a probabilistic flow prediction), (ii) to give a deterministic flow prediction, and (iii) to retrieve high-resolution data in the spatio-temporal domain from contaminated and/or under-sampled data.

Categories: Latest papers in fluid mechanics

### Sedimentation of general shaped particles using a multigrid fictitious boundary method

Physics of Fluids, Volume 32, Issue 6, June 2020.

In this paper, a direct numerical simulation technique, the Finite Element Fictitious Boundary Method (FBM), is used to simulate fluid–solid two-phase flows of different general shaped particles. The momentum interactions between solid and fluid phases are handled by using the FBM. The continuity and momentum equations are solved on a fixed Eulerian grid that is independent of flow features by using a discrete projection scheme inside a multi-grid finite element approach. A detailed description is presented for the geometric representation and modeling of two-dimensional particles of different general shapes, i.e., circular, elliptical, square, rectangular, triangular, and pentagonal shapes inside the fluid. We discussed the effects of particle shapes and the influences on the settling behavior of the particles. A comparison of the settling trajectories of the particles of the same mass but with different shapes is presented. Moreover, depending upon the particle’s shape, some interesting facts are discovered, which have a great influence on the particles’ trajectory and settling velocity. Some very important correlations between the drag force coefficient and particle’s Reynolds numbers with different density ratios of particles are obtained. Furthermore, we also studied the settling behavior of elliptical and rectangular particles with different axis ratios and a boomerang particle with different concave angles.

In this paper, a direct numerical simulation technique, the Finite Element Fictitious Boundary Method (FBM), is used to simulate fluid–solid two-phase flows of different general shaped particles. The momentum interactions between solid and fluid phases are handled by using the FBM. The continuity and momentum equations are solved on a fixed Eulerian grid that is independent of flow features by using a discrete projection scheme inside a multi-grid finite element approach. A detailed description is presented for the geometric representation and modeling of two-dimensional particles of different general shapes, i.e., circular, elliptical, square, rectangular, triangular, and pentagonal shapes inside the fluid. We discussed the effects of particle shapes and the influences on the settling behavior of the particles. A comparison of the settling trajectories of the particles of the same mass but with different shapes is presented. Moreover, depending upon the particle’s shape, some interesting facts are discovered, which have a great influence on the particles’ trajectory and settling velocity. Some very important correlations between the drag force coefficient and particle’s Reynolds numbers with different density ratios of particles are obtained. Furthermore, we also studied the settling behavior of elliptical and rectangular particles with different axis ratios and a boomerang particle with different concave angles.

Categories: Latest papers in fluid mechanics

### Wake topology and dynamics over a slender body at a high incidence and their relation to structural loading

Physics of Fluids, Volume 32, Issue 5, May 2020.

The flow over a slender cylindrical body with a hemisphere end was studied experimentally using a combination of force balance and time-resolved particle image velocity measurements. The investigation was performed at a subcritical Reynolds number (Re = 11 000) over a range of high incidence angles from 30° to 90°. The results show that significant cross-flow loading occurs for a range of incidence angles from 50° to 70°, with maximum mean and fluctuating loads taking place at 60°. Within this range of incidence angles, the loading has a bimodal nature, with intermittent switching between two states associated with the positive and negative cross-flow loading direction. The analysis of simultaneous force and wake measurements reveals that the two loading regimes are produced by two distinct wake topologies defined by strongly asymmetric vortex dynamics near the tip of the model. The results provide insight into salient features of the wake development and vortex dynamics and show that transient changes in the cross-flow force direction progress through a consistent change in the wake structure between two bounding quasi-steady states.

The flow over a slender cylindrical body with a hemisphere end was studied experimentally using a combination of force balance and time-resolved particle image velocity measurements. The investigation was performed at a subcritical Reynolds number (Re = 11 000) over a range of high incidence angles from 30° to 90°. The results show that significant cross-flow loading occurs for a range of incidence angles from 50° to 70°, with maximum mean and fluctuating loads taking place at 60°. Within this range of incidence angles, the loading has a bimodal nature, with intermittent switching between two states associated with the positive and negative cross-flow loading direction. The analysis of simultaneous force and wake measurements reveals that the two loading regimes are produced by two distinct wake topologies defined by strongly asymmetric vortex dynamics near the tip of the model. The results provide insight into salient features of the wake development and vortex dynamics and show that transient changes in the cross-flow force direction progress through a consistent change in the wake structure between two bounding quasi-steady states.

Categories: Latest papers in fluid mechanics

### Surface density function evolution and the influence of strain rates during turbulent boundary layer flashback of hydrogen-rich premixed combustion

Physics of Fluids, Volume 32, Issue 5, May 2020.

The statistical behavior of the magnitude of the reaction progress variable gradient [alternatively known as the surface density function (SDF)] and the strain rates, which govern the evolution of the SDF, have been analyzed for boundary layer flashback of a premixed hydrogen-air flame with an equivalence ratio of 1.5 in a fully developed turbulent channel flow. The non-reacting part of the channel flow is representative of the friction velocity based Reynolds number Reτ = 120. A skeletal chemical mechanism with nine chemical species and twenty reactions is employed to represent hydrogen-air combustion. Three definitions of the reaction progress variable (RPV) based on the mass fractions of H2, O2, and H2O have been considered to analyze the SDF statistics. It is found that the mean variations of the SDF and the displacement speed Sd depend on the choice of the RPV and the distance away from the wall. The preferential alignment of the RPV gradient with the most extensive principal strain rate strengthens with an increase in distance from the cold wall, which leads to changes in the behaviors of normal and tangential strain rates from the vicinity of the wall toward the middle of the channel. The differences in displacement speed statistics for different choices of the RPV and the wall distance affect the behaviors of the normal strain rate due to flame propagation and curvature stretch. The relative thickening/thinning of the reaction layers of the major species has been explained in terms of the statistics of the effective normal strain rate experienced by the progress variable isosurfaces for different wall distances and choices of RPVs.

The statistical behavior of the magnitude of the reaction progress variable gradient [alternatively known as the surface density function (SDF)] and the strain rates, which govern the evolution of the SDF, have been analyzed for boundary layer flashback of a premixed hydrogen-air flame with an equivalence ratio of 1.5 in a fully developed turbulent channel flow. The non-reacting part of the channel flow is representative of the friction velocity based Reynolds number Reτ = 120. A skeletal chemical mechanism with nine chemical species and twenty reactions is employed to represent hydrogen-air combustion. Three definitions of the reaction progress variable (RPV) based on the mass fractions of H2, O2, and H2O have been considered to analyze the SDF statistics. It is found that the mean variations of the SDF and the displacement speed Sd depend on the choice of the RPV and the distance away from the wall. The preferential alignment of the RPV gradient with the most extensive principal strain rate strengthens with an increase in distance from the cold wall, which leads to changes in the behaviors of normal and tangential strain rates from the vicinity of the wall toward the middle of the channel. The differences in displacement speed statistics for different choices of the RPV and the wall distance affect the behaviors of the normal strain rate due to flame propagation and curvature stretch. The relative thickening/thinning of the reaction layers of the major species has been explained in terms of the statistics of the effective normal strain rate experienced by the progress variable isosurfaces for different wall distances and choices of RPVs.

Categories: Latest papers in fluid mechanics

### Symmetry breaking phenomena in thermovibrationally driven particle accumulation structures

Physics of Fluids, Volume 32, Issue 5, May 2020.

Following the recent discovery of new three-dimensional particle attractors driven by joint (fluid) thermovibrational and (particle) inertial effects in closed cavities with various shapes and symmetries [M. Lappa, Phys. Fluids 26(9), 093301 (2014); ibid. 31(7), 073303 (2019)], the present analysis continues this line of inquiry by probing influential factors hitherto not considered; among them, the role of the steady component of thermovibrational convection, i.e., the time-averaged velocity field that is developed by the fluid due to the non-linear nature of the overarching balance equations. It is shown how this apparently innocuous problem opens up a vast parameter space, which includes several variables, comprising (but not limited to) the frequency of vibrations, the so-called “Gershuni number,” the size of particles (Stokes number), and their relative density with respect to the surrounding fluid (density ratio). A variety of new particle structures (2D and 3D) are uncovered and a complete analysis of their morphology is presented. The results reveal an increase in the multiplicity of solutions brought in by the counter-intuitive triadic relationship among particle inertial effects and the instantaneous and time-averaged convective thermovibrational phenomena. Finally, a universal formula is provided that is able to predict correctly the time required for the formation of all the observed structures.

Following the recent discovery of new three-dimensional particle attractors driven by joint (fluid) thermovibrational and (particle) inertial effects in closed cavities with various shapes and symmetries [M. Lappa, Phys. Fluids 26(9), 093301 (2014); ibid. 31(7), 073303 (2019)], the present analysis continues this line of inquiry by probing influential factors hitherto not considered; among them, the role of the steady component of thermovibrational convection, i.e., the time-averaged velocity field that is developed by the fluid due to the non-linear nature of the overarching balance equations. It is shown how this apparently innocuous problem opens up a vast parameter space, which includes several variables, comprising (but not limited to) the frequency of vibrations, the so-called “Gershuni number,” the size of particles (Stokes number), and their relative density with respect to the surrounding fluid (density ratio). A variety of new particle structures (2D and 3D) are uncovered and a complete analysis of their morphology is presented. The results reveal an increase in the multiplicity of solutions brought in by the counter-intuitive triadic relationship among particle inertial effects and the instantaneous and time-averaged convective thermovibrational phenomena. Finally, a universal formula is provided that is able to predict correctly the time required for the formation of all the observed structures.

Categories: Latest papers in fluid mechanics

### Investigation of asymmetrically pitching airfoil at high reduced frequency

Physics of Fluids, Volume 32, Issue 5, May 2020.

The expanding application in micro-air vehicles has encouraged many researchers to understand the unsteady flow around a flapping foil at a low Reynolds number. We numerically investigate an incompressible unsteady flow around a two-dimensional pitching airfoil (SD7003) at high reduced frequency (k ≥ 3) in the laminar regime. This study interrogates the effect of different unsteady parameters, namely, amplitude (A), reduced frequency (k), Reynolds number (Re), and asymmetry parameter (S) for pitching motion on the force coefficients. The inviscid theoretical model is utilized to calculate the lift coefficient for sinusoidal motion in the viscous regime, and a comparison is made with the numerical results. The theoretical analysis identifies the influence of the non-circulatory lift over circulatory lift at a high reduced frequency. Furthermore, the results indicate that the reduced frequency (k) and asymmetry parameter (S) have a significant impact on the instantaneous and time-averaged force coefficients as well as on the vortex structure in the wake. Finally, the fast Fourier transformation analysis is carried out over a simulated case with fixed amplitude and Reynolds number for distinct k and S values. The findings confirm that the dominant frequency in the flow (k*) has a direct correlation to the airfoil pitching frequency (k).

The expanding application in micro-air vehicles has encouraged many researchers to understand the unsteady flow around a flapping foil at a low Reynolds number. We numerically investigate an incompressible unsteady flow around a two-dimensional pitching airfoil (SD7003) at high reduced frequency (k ≥ 3) in the laminar regime. This study interrogates the effect of different unsteady parameters, namely, amplitude (A), reduced frequency (k), Reynolds number (Re), and asymmetry parameter (S) for pitching motion on the force coefficients. The inviscid theoretical model is utilized to calculate the lift coefficient for sinusoidal motion in the viscous regime, and a comparison is made with the numerical results. The theoretical analysis identifies the influence of the non-circulatory lift over circulatory lift at a high reduced frequency. Furthermore, the results indicate that the reduced frequency (k) and asymmetry parameter (S) have a significant impact on the instantaneous and time-averaged force coefficients as well as on the vortex structure in the wake. Finally, the fast Fourier transformation analysis is carried out over a simulated case with fixed amplitude and Reynolds number for distinct k and S values. The findings confirm that the dominant frequency in the flow (k*) has a direct correlation to the airfoil pitching frequency (k).

Categories: Latest papers in fluid mechanics

### Droplet deformation and breakup in shear flow of air

Physics of Fluids, Volume 32, Issue 5, May 2020.

The deformation and breakup of droplets in airflows is important in many applications of spray and atomization processes. However, the shear effect of airflow has never been reported. In this study, the deformation and breakup of droplets in the shear flow of air is investigated experimentally using high-speed imaging, digital image processing, and particle image velocimetry. We identify a new breakup mode of droplets, i.e., the butterfly breakup, in which the strong aerodynamic pressure on the lower part of the droplet leads to the deflection of the droplet and then the formation of a butterfly-shaped bag. A regime map of the droplet breakup is produced, and the transitions between different modes are obtained based on scaling analysis. The elongation and the fragmentation of the droplet rim are analyzed, and the results show that they are significantly affected by the shear via the formation and the growth of nodes on the rim.

The deformation and breakup of droplets in airflows is important in many applications of spray and atomization processes. However, the shear effect of airflow has never been reported. In this study, the deformation and breakup of droplets in the shear flow of air is investigated experimentally using high-speed imaging, digital image processing, and particle image velocimetry. We identify a new breakup mode of droplets, i.e., the butterfly breakup, in which the strong aerodynamic pressure on the lower part of the droplet leads to the deflection of the droplet and then the formation of a butterfly-shaped bag. A regime map of the droplet breakup is produced, and the transitions between different modes are obtained based on scaling analysis. The elongation and the fragmentation of the droplet rim are analyzed, and the results show that they are significantly affected by the shear via the formation and the growth of nodes on the rim.

Categories: Latest papers in fluid mechanics

### Effect of suction on laminar-flow control in subsonic boundary layers with forward-/backward-facing steps

Physics of Fluids, Volume 32, Issue 5, May 2020.

In a subsonic boundary layer, a forward-facing step (FFS) or a backward-facing step (BFS) usually destabilizes the oncoming Tollmien–Schlichting (T-S) waves, leading to a promotion of laminar–turbulent transition. This paper studies a laminar-flow control strategy by introducing wall suction immediately ahead of the FFS or behind the BFS. The impact of the step–suction combination on an oncoming T-S wave is quantified by a transmission coefficient, defined as the ratio of the asymptotic amplitude downstream of the step and suction to that upstream. In order to solve this problem, a local scattering theory based on the large-Reynolds number (large-R) asymptotic framework and a Harmonic linearized Navier–Stokes approach, that calculates the perturbation field at finite Reynolds numbers, are employed. The latter approach is confirmed to be accurate by comparing its results with direct numerical simulations, and the results given by the two approaches agree when the Reynolds number is asymptotically large. According to the large-R triple-deck formulism, a few control parameters, such as the Mach number, Reynolds number, and wall temperature, disappear, which makes a systematical parametric study possible. The destabilizing effect of a step increases with its height, while the stabilizing effect of suction increases with its flux. For a step with a moderate height, suction with a small flux is sufficient to compensate the destabilizing effect of the step.

In a subsonic boundary layer, a forward-facing step (FFS) or a backward-facing step (BFS) usually destabilizes the oncoming Tollmien–Schlichting (T-S) waves, leading to a promotion of laminar–turbulent transition. This paper studies a laminar-flow control strategy by introducing wall suction immediately ahead of the FFS or behind the BFS. The impact of the step–suction combination on an oncoming T-S wave is quantified by a transmission coefficient, defined as the ratio of the asymptotic amplitude downstream of the step and suction to that upstream. In order to solve this problem, a local scattering theory based on the large-Reynolds number (large-R) asymptotic framework and a Harmonic linearized Navier–Stokes approach, that calculates the perturbation field at finite Reynolds numbers, are employed. The latter approach is confirmed to be accurate by comparing its results with direct numerical simulations, and the results given by the two approaches agree when the Reynolds number is asymptotically large. According to the large-R triple-deck formulism, a few control parameters, such as the Mach number, Reynolds number, and wall temperature, disappear, which makes a systematical parametric study possible. The destabilizing effect of a step increases with its height, while the stabilizing effect of suction increases with its flux. For a step with a moderate height, suction with a small flux is sufficient to compensate the destabilizing effect of the step.

Categories: Latest papers in fluid mechanics

### Experimental and numerical study of effect of secondary surfaces fixed over rectangular vortex generator with an overview of dynamic mode decomposition

Physics of Fluids, Volume 32, Issue 5, May 2020.

Addition of a vortex generator (VG) to the heated surface creates longitudinal vortices in the flow; however, it induces drag. Surface modification of the VG may play a role in the thermal performance of the system. Therefore, flow and thermal behavior are studied for a secondary surface (SS) attached to the primary surface of a rectangular VG, which is placed inside a rectangular channel using air at Re = 5000. The VG with the SS is compared with a conventional rectangular VG having volume constant. With the addition of SS, the flow behind the VG greatly shears the produced primary vortex (P), which results in stretching. Stretching increases the angular momentum of the vortex with the decrease in the span of the produced vortices. The interaction between the co-rotating vortices P and high pressure side horse-shoe vortex (Hp) shows that the higher strain field induced by the vortex P shears away the vortex Hp. The vortex P developed under the influence of SS induces a higher degree of tilting toward the heated surface with low propagation speed. Finally, the dynamic decomposition of the vortices in the channel reveals that the vortex P appears to be dominant.

Addition of a vortex generator (VG) to the heated surface creates longitudinal vortices in the flow; however, it induces drag. Surface modification of the VG may play a role in the thermal performance of the system. Therefore, flow and thermal behavior are studied for a secondary surface (SS) attached to the primary surface of a rectangular VG, which is placed inside a rectangular channel using air at Re = 5000. The VG with the SS is compared with a conventional rectangular VG having volume constant. With the addition of SS, the flow behind the VG greatly shears the produced primary vortex (P), which results in stretching. Stretching increases the angular momentum of the vortex with the decrease in the span of the produced vortices. The interaction between the co-rotating vortices P and high pressure side horse-shoe vortex (Hp) shows that the higher strain field induced by the vortex P shears away the vortex Hp. The vortex P developed under the influence of SS induces a higher degree of tilting toward the heated surface with low propagation speed. Finally, the dynamic decomposition of the vortices in the channel reveals that the vortex P appears to be dominant.

Categories: Latest papers in fluid mechanics

### Analysis of flow characteristics downstream delta-winglet vortex generator using stereoscopic particle image velocimetry for laminar, transitional, and turbulent channel flow regimes

Physics of Fluids, Volume 32, Issue 5, May 2020.

The evolution of flow structures downstream a single pair of delta-winglet vortex generators (VGs) is investigated experimentally using stereoscopic particle image velocimetry. In addition, the laser Doppler anemometer technique is performed to characterize the upstream flow. Experiments are conducted in a bounded channel flow (height H) for the Reynolds numbers (ReDH, based on the hydraulic diameter height) ranging from 400 to 12 000. The purpose of this study is to provide detail insight into the generation and the dissipation of longitudinal vortices over a wide flow regime range including the laminar–turbulent transition. With a focus on transverse sections, the flow field is detailed. For all flow regimes, the main flow topology shows that the two main counter-rotating vortices are generated at a certain streamwise distance downstream the VG and then are advected gradually toward the channel lateral-walls. A secondary vortex pair is induced closer to the wall. Our results show that close to the VGs, local regions (1 > z/H > −1) are strongly defined as the inception of the turbulence production. The intensity of this latter is shown to vanish beyond a certain distance far from the origin of the perturbation (when x/H is greater than 3). The instantaneous flow structure describes the mechanism of vortex generation, relying on the intermittence of the flow organization and the sweep and ejection event balance. Detailed analysis on the turbulence properties and wall shear stress has been assessed and revealed that the flow transition induced by the perturbation of the VG is achieved at a Reynolds number no greater than 1500.

The evolution of flow structures downstream a single pair of delta-winglet vortex generators (VGs) is investigated experimentally using stereoscopic particle image velocimetry. In addition, the laser Doppler anemometer technique is performed to characterize the upstream flow. Experiments are conducted in a bounded channel flow (height H) for the Reynolds numbers (ReDH, based on the hydraulic diameter height) ranging from 400 to 12 000. The purpose of this study is to provide detail insight into the generation and the dissipation of longitudinal vortices over a wide flow regime range including the laminar–turbulent transition. With a focus on transverse sections, the flow field is detailed. For all flow regimes, the main flow topology shows that the two main counter-rotating vortices are generated at a certain streamwise distance downstream the VG and then are advected gradually toward the channel lateral-walls. A secondary vortex pair is induced closer to the wall. Our results show that close to the VGs, local regions (1 > z/H > −1) are strongly defined as the inception of the turbulence production. The intensity of this latter is shown to vanish beyond a certain distance far from the origin of the perturbation (when x/H is greater than 3). The instantaneous flow structure describes the mechanism of vortex generation, relying on the intermittence of the flow organization and the sweep and ejection event balance. Detailed analysis on the turbulence properties and wall shear stress has been assessed and revealed that the flow transition induced by the perturbation of the VG is achieved at a Reynolds number no greater than 1500.

Categories: Latest papers in fluid mechanics

### Stability of flow in a deformable channel with an unrestrained boundary

Physics of Fluids, Volume 32, Issue 5, May 2020.

We report results from a linear stability analysis of Newtonian plane Poiseuille flow through a deformable linear elastic channel with an unrestrained boundary wherein the deformable wall is not rigidly bonded to a substrate and is free to undergo motion. The objective of this study is to address the experimental observations of instabilities for this configuration [S. S. Srinivas and V. Kumaran, “Transitions to different kinds of turbulence in a channel with soft walls,” J. Fluid Mech. 822, 267–306 (2017)]. We analyze the role of an unrestrained deformable boundary on the stability of channel flow using both asymptotic and numerical methods. Our results show that when the solid to fluid layer thickness ratio is O(1), both wall modes (whose critical Reynolds number Rec ∝ G3/4, with G being the shear modulus of the solid) and inviscid modes (whose Rec ∝ G1/2) are significantly destabilized by the presence of an unrestrained boundary when compared to channels with completely bonded deformable boundaries. In agreement with experimental observations, the eigenfunctions corresponding to both these unstable modes exhibit a pronounced asymmetric behavior, thereby highlighting the influence of the unrestrained deformable boundary on the stability of the flow. The asymptotic predictions for the wall mode instability are shown to be in excellent agreement with our numerical results. However, for the solid to fluid thickness ratio ∼7.7 (used in the aforementioned experiments), our results show that the reduction in the critical Reynolds number due to the unrestrained boundary is only moderate; we provide possible reasons for the same.

We report results from a linear stability analysis of Newtonian plane Poiseuille flow through a deformable linear elastic channel with an unrestrained boundary wherein the deformable wall is not rigidly bonded to a substrate and is free to undergo motion. The objective of this study is to address the experimental observations of instabilities for this configuration [S. S. Srinivas and V. Kumaran, “Transitions to different kinds of turbulence in a channel with soft walls,” J. Fluid Mech. 822, 267–306 (2017)]. We analyze the role of an unrestrained deformable boundary on the stability of channel flow using both asymptotic and numerical methods. Our results show that when the solid to fluid layer thickness ratio is O(1), both wall modes (whose critical Reynolds number Rec ∝ G3/4, with G being the shear modulus of the solid) and inviscid modes (whose Rec ∝ G1/2) are significantly destabilized by the presence of an unrestrained boundary when compared to channels with completely bonded deformable boundaries. In agreement with experimental observations, the eigenfunctions corresponding to both these unstable modes exhibit a pronounced asymmetric behavior, thereby highlighting the influence of the unrestrained deformable boundary on the stability of the flow. The asymptotic predictions for the wall mode instability are shown to be in excellent agreement with our numerical results. However, for the solid to fluid thickness ratio ∼7.7 (used in the aforementioned experiments), our results show that the reduction in the critical Reynolds number due to the unrestrained boundary is only moderate; we provide possible reasons for the same.

Categories: Latest papers in fluid mechanics