# 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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### MHD mixed convection and entropy generation of nanofluid in a lid-driven U-shaped cavity with internal heat and partial slip

Physics of Fluids, Volume 31, Issue 4, April 2019.

This contribution simulates the impact of partial slip on entropy generation due to magnetohydrodynamic, mixed convection of nanofluids in a lid-driven U-shaped cavity with discrete heating. The influence of the partial slip effect is proposed along the lid-driven vertical walls. A uniform heat flux source on the bottom wall is proposed; meanwhile, the two portions of the outer-upper horizontal walls are cooled isothermally. The remainder cavity walls are taken adiabatic. The governing equations are solved using the finite volume approach, and the outcomes are successfully validated against previous studies. Simulation results are presented and discussed for several cases with the impacts of the governing parameters on the heat transfer rate. Inspection of the results in mixed convective and entropy generation environments demonstrate that the average Nusselt number increases with the increase in the volume fraction of nanoparticles at AR = 0.1. For all values of D (heat source location), the Nusselt number increases by crossing the heat source and reaches its maximum value at the end of the source. Also, for all values of the aspect ratio, addition of nanoparticles into the base fluid leads to a loss in the thermal performance. Moreover, for all states of movement, addition of nanoparticles into the base fluid leads to an increase in the entropy.

This contribution simulates the impact of partial slip on entropy generation due to magnetohydrodynamic, mixed convection of nanofluids in a lid-driven U-shaped cavity with discrete heating. The influence of the partial slip effect is proposed along the lid-driven vertical walls. A uniform heat flux source on the bottom wall is proposed; meanwhile, the two portions of the outer-upper horizontal walls are cooled isothermally. The remainder cavity walls are taken adiabatic. The governing equations are solved using the finite volume approach, and the outcomes are successfully validated against previous studies. Simulation results are presented and discussed for several cases with the impacts of the governing parameters on the heat transfer rate. Inspection of the results in mixed convective and entropy generation environments demonstrate that the average Nusselt number increases with the increase in the volume fraction of nanoparticles at AR = 0.1. For all values of D (heat source location), the Nusselt number increases by crossing the heat source and reaches its maximum value at the end of the source. Also, for all values of the aspect ratio, addition of nanoparticles into the base fluid leads to a loss in the thermal performance. Moreover, for all states of movement, addition of nanoparticles into the base fluid leads to an increase in the entropy.

Categories: Latest papers in fluid mechanics

### Effects of individual horizontal distance on the three-dimensional bionic flapping multi-wings in different schooling configurations

Physics of Fluids, Volume 31, Issue 4, April 2019.

After billions of years of natural selection, flying animals with flapping wings have superior flight and mobility capabilities. The aerodynamic characteristics and the propulsion mechanism of bionic wings have attracted a large number of researchers because they will be beneficial to novel bio-inspired micro air or underwater vehicle design. Except the single activities, for fish, birds, and insects, there is a very popular and interesting biological clustering phenomenon known as schooling. Considering the real biological movements in schooling under low Reynolds number, the study of the flow mechanisms and thrust performance of bionic multiflapping wings in different schooling configurations could be applied to the design of future bionic flapping wing aircraft formation. The unsteady flow mechanisms and the thrust performance of three-dimensional multiflapping wings in three different schooling configurations are numerically investigated using the immersed boundary-lattice Boltzmann method with the Chinese TianHe-II supercomputer. The influences of different schooling configurations and individual distances on the thrust performance of multiflapping wings are thoroughly investigated. Numerical results indicate that the individual horizontal distance has great effects on the thrust performance of multiflapping wings in schooling, and the average thrust coefficient of each flapping wing in different schooling configurations at a specific individual horizontal distance is larger than that of the single flapping wing. There is an optimum distance for different schooling configurations, where the individual interaction lead to best propulsion performance. Different from the simple tandem schooling, the closer the individual distance, the better the overall thrust performance obtained for triangle and diamond schooling.

After billions of years of natural selection, flying animals with flapping wings have superior flight and mobility capabilities. The aerodynamic characteristics and the propulsion mechanism of bionic wings have attracted a large number of researchers because they will be beneficial to novel bio-inspired micro air or underwater vehicle design. Except the single activities, for fish, birds, and insects, there is a very popular and interesting biological clustering phenomenon known as schooling. Considering the real biological movements in schooling under low Reynolds number, the study of the flow mechanisms and thrust performance of bionic multiflapping wings in different schooling configurations could be applied to the design of future bionic flapping wing aircraft formation. The unsteady flow mechanisms and the thrust performance of three-dimensional multiflapping wings in three different schooling configurations are numerically investigated using the immersed boundary-lattice Boltzmann method with the Chinese TianHe-II supercomputer. The influences of different schooling configurations and individual distances on the thrust performance of multiflapping wings are thoroughly investigated. Numerical results indicate that the individual horizontal distance has great effects on the thrust performance of multiflapping wings in schooling, and the average thrust coefficient of each flapping wing in different schooling configurations at a specific individual horizontal distance is larger than that of the single flapping wing. There is an optimum distance for different schooling configurations, where the individual interaction lead to best propulsion performance. Different from the simple tandem schooling, the closer the individual distance, the better the overall thrust performance obtained for triangle and diamond schooling.

Categories: Latest papers in fluid mechanics

### Convective and absolute instability of viscoelastic liquid jets in the presence of gravity

Physics of Fluids, Volume 31, Issue 4, April 2019.

The convective and absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of a viscoelastic liquid jet. An asymptotic approach, based on the slenderness of the jet, is used to obtain the steady state solutions. By considering traveling wave modes, we derive a dispersion relation relating the frequency to the wavenumber of disturbances which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters, including the Froude number, on convective and absolute instability. In this work, we use a mapping technique developed by Kupfer, Bers, and Ram [“The cusp map in the complex-frequency plane for absolute instabilities,” Phys. Fluids 30, 3075–3082 (1987)] to find the cusp point in the complex frequency plane and its corresponding saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes.

The convective and absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of a viscoelastic liquid jet. An asymptotic approach, based on the slenderness of the jet, is used to obtain the steady state solutions. By considering traveling wave modes, we derive a dispersion relation relating the frequency to the wavenumber of disturbances which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters, including the Froude number, on convective and absolute instability. In this work, we use a mapping technique developed by Kupfer, Bers, and Ram [“The cusp map in the complex-frequency plane for absolute instabilities,” Phys. Fluids 30, 3075–3082 (1987)] to find the cusp point in the complex frequency plane and its corresponding saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes.

Categories: Latest papers in fluid mechanics

### A dynamic closure modeling framework for model order reduction of geophysical flows

Physics of Fluids, Volume 31, Issue 4, April 2019.

In this paper, a dynamic closure modeling approach has been derived to stabilize the projection-based reduced order models in the long-term evolution of forced-dissipative dynamical systems. To simplify our derivation without losing generalizability, the proposed reduced order modeling (ROM) framework is first constructed by Galerkin projection of the single-layer quasigeostrophic equation, a standard prototype of large-scale general circulation models, onto a set of dominant proper orthogonal decomposition modes. We then propose an eddy viscosity closure approach to stabilize the resulting surrogate model considering the analogy between large eddy simulation (LES) and truncated modal projection. Our efforts, in particular, include the translation of the dynamic subgrid-scale model into our ROM setting by defining a test truncation similar to the test filtering in LES. The a posteriori analysis shows that our approach is remarkably accurate, allowing us to integrate simulations over long time intervals at a nominally small computational overhead.

In this paper, a dynamic closure modeling approach has been derived to stabilize the projection-based reduced order models in the long-term evolution of forced-dissipative dynamical systems. To simplify our derivation without losing generalizability, the proposed reduced order modeling (ROM) framework is first constructed by Galerkin projection of the single-layer quasigeostrophic equation, a standard prototype of large-scale general circulation models, onto a set of dominant proper orthogonal decomposition modes. We then propose an eddy viscosity closure approach to stabilize the resulting surrogate model considering the analogy between large eddy simulation (LES) and truncated modal projection. Our efforts, in particular, include the translation of the dynamic subgrid-scale model into our ROM setting by defining a test truncation similar to the test filtering in LES. The a posteriori analysis shows that our approach is remarkably accurate, allowing us to integrate simulations over long time intervals at a nominally small computational overhead.

Categories: Latest papers in fluid mechanics

### Solute transport in two-zone packed tube flow: Long-time asymptotic expansion

Physics of Fluids, Volume 31, Issue 4, April 2019.

Previous studies of solute transport in two-zone packed tube flows focused only on the cross-sectional mean concentration, a Gaussian distribution with advection velocity and Taylor dispersivity. This work analytically investigates the complete spatial concentration distribution. The two-dimensional (longitudinal and transverse) concentration distribution is obtained, by Chatwin’s long-time asymptotic technique: Edgeworth expansion. Non-Gaussian distribution effects like skewness and kurtosis are included in the asymptotic solution. Three cases with different porosity distributions between zones are studied to illustrate the impact of heterogeneity of media distributions on solute dispersion. The variation of porosity distributions can lead to great changes in velocity profiles, positions of local maxima of the concentration distribution, and basic characteristics of the cross-sectional mean concentration distribution, such as dispersivity, skewness, and kurtosis. Additionally, zones have largely different in zone-cross-sectional mean concentration distributions in the initial stage of solute transport.

Previous studies of solute transport in two-zone packed tube flows focused only on the cross-sectional mean concentration, a Gaussian distribution with advection velocity and Taylor dispersivity. This work analytically investigates the complete spatial concentration distribution. The two-dimensional (longitudinal and transverse) concentration distribution is obtained, by Chatwin’s long-time asymptotic technique: Edgeworth expansion. Non-Gaussian distribution effects like skewness and kurtosis are included in the asymptotic solution. Three cases with different porosity distributions between zones are studied to illustrate the impact of heterogeneity of media distributions on solute dispersion. The variation of porosity distributions can lead to great changes in velocity profiles, positions of local maxima of the concentration distribution, and basic characteristics of the cross-sectional mean concentration distribution, such as dispersivity, skewness, and kurtosis. Additionally, zones have largely different in zone-cross-sectional mean concentration distributions in the initial stage of solute transport.

Categories: Latest papers in fluid mechanics

### Near-bed turbulence structures in water-worked and screeded gravel-bed flows

Physics of Fluids, Volume 31, Issue 4, April 2019.

Coherent structures and their impact on the near-bed time-averaged flow structure in a water-worked gravel-bed (WGB) and a screeded gravel-bed (SGB) are analyzed. Instantaneous velocities were measured using a particle image velocimetry system in the WGB and SGB flows in a flume with rectangular cross section. To ascertain the response of the WGB with respect to the SGB to the coherent structures, the time- and double-averaged flow, and the spatially averaged (SA) turbulence parameters, the experimental flow conditions for both the beds were kept identical. The surface gravels in the WGB were spatially organized owing to the water action. By contrast, the surface gravels in the SGB were randomly poised. These result in a higher roughness height in the WGB than in the SGB. Time series analysis for the instantaneous velocity and vorticity on a central vertical plane along the streamwise direction proves that the coherent structures in the near-bed flow zone are constituted by rapidly and slowly moving fluid streaks. Besides, the time-averaged streamwise velocity, vorticity, turbulence level, third-order correlations, and turbulent kinetic energy (TKE) budget are analyzed in the WGB and SGB. Their contours are plotted on the central vertical plane to study their spatial distributions. In addition, the SA higher-order correlations and TKE budget in the WGB and SGB are examined. A comparative study infers that the higher roughness in the WGB than in the SGB causes both the time-averaged and SA turbulence parameters in the former to be greater than those in the latter.

Coherent structures and their impact on the near-bed time-averaged flow structure in a water-worked gravel-bed (WGB) and a screeded gravel-bed (SGB) are analyzed. Instantaneous velocities were measured using a particle image velocimetry system in the WGB and SGB flows in a flume with rectangular cross section. To ascertain the response of the WGB with respect to the SGB to the coherent structures, the time- and double-averaged flow, and the spatially averaged (SA) turbulence parameters, the experimental flow conditions for both the beds were kept identical. The surface gravels in the WGB were spatially organized owing to the water action. By contrast, the surface gravels in the SGB were randomly poised. These result in a higher roughness height in the WGB than in the SGB. Time series analysis for the instantaneous velocity and vorticity on a central vertical plane along the streamwise direction proves that the coherent structures in the near-bed flow zone are constituted by rapidly and slowly moving fluid streaks. Besides, the time-averaged streamwise velocity, vorticity, turbulence level, third-order correlations, and turbulent kinetic energy (TKE) budget are analyzed in the WGB and SGB. Their contours are plotted on the central vertical plane to study their spatial distributions. In addition, the SA higher-order correlations and TKE budget in the WGB and SGB are examined. A comparative study infers that the higher roughness in the WGB than in the SGB causes both the time-averaged and SA turbulence parameters in the former to be greater than those in the latter.

Categories: Latest papers in fluid mechanics

### Drop impacting on a single layer of particles: Evolution of ring without particles

Physics of Fluids, Volume 31, Issue 4, April 2019.

In this study, we examined the impacts of a millimeter sized water drop hitting a layer of uniformly distributed particles on a hydrophilic/hydrophobic glass slide. A ring/disc structure without particles was formed and modified by two mechanisms: pushout and pullback. The pushout factor dominated the process when the drop hit on the hydrophilic glass slide, while the pullback factor played a decisive role during impact on the hydrophobic surface. The rebound of a drop on the hydrophobic surface formed a disc-shaped ring. We showed that the ratio of the effects of these two factors on the ring/disc width were independent from the impact speed, in both experimental and scaling analyses. Our results also suggested that higher hydrophobicity of a water drop on the hydrophobic glass slide, instead of a polymethyl methacrylate (PMMA) particle surface, resulted in a lower maximum spreading distance when the drop hit the PMMA particle layer on a hydrophobic surface.

In this study, we examined the impacts of a millimeter sized water drop hitting a layer of uniformly distributed particles on a hydrophilic/hydrophobic glass slide. A ring/disc structure without particles was formed and modified by two mechanisms: pushout and pullback. The pushout factor dominated the process when the drop hit on the hydrophilic glass slide, while the pullback factor played a decisive role during impact on the hydrophobic surface. The rebound of a drop on the hydrophobic surface formed a disc-shaped ring. We showed that the ratio of the effects of these two factors on the ring/disc width were independent from the impact speed, in both experimental and scaling analyses. Our results also suggested that higher hydrophobicity of a water drop on the hydrophobic glass slide, instead of a polymethyl methacrylate (PMMA) particle surface, resulted in a lower maximum spreading distance when the drop hit the PMMA particle layer on a hydrophobic surface.

Categories: Latest papers in fluid mechanics

### The theory and application of eulerlets

Physics of Fluids, Volume 31, Issue 4, April 2019.

Consider a fixed body in a uniform flow field in the limit as the Reynolds number approaches infinity and the flow field remains steady. Instead of using standard techniques and theory for describing the problem, a new method is employed based upon the concept of matching two different Green’s integral representations over a common boundary, one given by approximations valid in the near-field and the other by approximations in the far-field. Further novelty arises from the choice of a near-field, that is, the Euler flow matched to an Oseen flow far-field. This entails introducing and defining eulerlets that are Green’s functions of the Euler equation. One important consequence of the model is the presence of a new Euler wake velocity not captured in standard models. This has a constant unchanging downstream profile and arises from the matching to the far-field Oseen wake velocity. It is then shown how this representation reduces to classical inviscid ideal flow aerodynamics when applied to flow past aerofoils and wings. It is also shown how it reduces to slender body flow theory. Finally, the formulation is tested on uniform flow past a circular cylinder for mean-steady subcritical laminar flow and turbulent flow. The inviscid impermeability boundary condition is used, the drag coefficient is specified, and a constant distribution of drag eulerlets is modeled. The forward flow separation and pressure drop in the wake are captured and compare favorably with experiment. The future expectation is the modeling of multiple general shaped bodies.

Consider a fixed body in a uniform flow field in the limit as the Reynolds number approaches infinity and the flow field remains steady. Instead of using standard techniques and theory for describing the problem, a new method is employed based upon the concept of matching two different Green’s integral representations over a common boundary, one given by approximations valid in the near-field and the other by approximations in the far-field. Further novelty arises from the choice of a near-field, that is, the Euler flow matched to an Oseen flow far-field. This entails introducing and defining eulerlets that are Green’s functions of the Euler equation. One important consequence of the model is the presence of a new Euler wake velocity not captured in standard models. This has a constant unchanging downstream profile and arises from the matching to the far-field Oseen wake velocity. It is then shown how this representation reduces to classical inviscid ideal flow aerodynamics when applied to flow past aerofoils and wings. It is also shown how it reduces to slender body flow theory. Finally, the formulation is tested on uniform flow past a circular cylinder for mean-steady subcritical laminar flow and turbulent flow. The inviscid impermeability boundary condition is used, the drag coefficient is specified, and a constant distribution of drag eulerlets is modeled. The forward flow separation and pressure drop in the wake are captured and compare favorably with experiment. The future expectation is the modeling of multiple general shaped bodies.

Categories: Latest papers in fluid mechanics

### The physics of twin-fluid jet-in-crossflow at atmospheric and jet-engine operating conditions

Physics of Fluids, Volume 31, Issue 4, April 2019.

Efforts to mitigate jet engine emissions produced a class of swirl-stabilized combustors in which a rich pilot-flame in the center of the swirl-cup anchors an outer-annulus of lean-premixed main-flame. Fuel distribution within the annulus must be carefully controlled to allow stable combustion while avoiding excessive swirl-cup heating and flashbacks. This was traditionally achieved by placing plain jet-in-crossflow (JICF) fuel injectors around the swirl-cup; however, a recent increase in engine operating pressure and temperature along with demand for leaner fuel-air mixtures made the traditional approach untenable. Hence, modern swirl-cup designs begin to adopt a new fuel-injection technique called the “twin-fluid JICF (TF-JICF)” where a sleeve of air is co-injected with the liquid jet to modify its spray-pattern. TF-JICF is a nascent variation of the JICF that is not well understood, especially at elevated pressures. Hence, an experimental investigation of TF-JICF spray behaviors was performed by our group, covering the operating conditions of 1.5–9.5 atm in crossflow pressure, 175–1050 in crossflow Weber number, 5–40 in momentum flux-ratio, and 0%–150% in air-nozzle pressure-drop, at the crossflow temperature of 150 °C and velocity of 75 m/s. Part 1 of the investigation’s results, which identified four distinct flow regimes and nonmonotonic penetration trends in TF-JICF, was published in the work of Tan et al., “The regimes of twin-fluid jet-in-crossflow at atmospheric and jet-engine operating conditions,” Phy. Fluids 30, 025101 (2018). The current paper expands upon the previous report by elucidating key spray features and potential mechanisms (e.g., transitions between crossflow-driven atomization, air-driven shear-atomization, and air-driven prompt-atomization) within each TF-JICF regime, thereby providing a conceptual framework of TF-JICF for future studies.

Efforts to mitigate jet engine emissions produced a class of swirl-stabilized combustors in which a rich pilot-flame in the center of the swirl-cup anchors an outer-annulus of lean-premixed main-flame. Fuel distribution within the annulus must be carefully controlled to allow stable combustion while avoiding excessive swirl-cup heating and flashbacks. This was traditionally achieved by placing plain jet-in-crossflow (JICF) fuel injectors around the swirl-cup; however, a recent increase in engine operating pressure and temperature along with demand for leaner fuel-air mixtures made the traditional approach untenable. Hence, modern swirl-cup designs begin to adopt a new fuel-injection technique called the “twin-fluid JICF (TF-JICF)” where a sleeve of air is co-injected with the liquid jet to modify its spray-pattern. TF-JICF is a nascent variation of the JICF that is not well understood, especially at elevated pressures. Hence, an experimental investigation of TF-JICF spray behaviors was performed by our group, covering the operating conditions of 1.5–9.5 atm in crossflow pressure, 175–1050 in crossflow Weber number, 5–40 in momentum flux-ratio, and 0%–150% in air-nozzle pressure-drop, at the crossflow temperature of 150 °C and velocity of 75 m/s. Part 1 of the investigation’s results, which identified four distinct flow regimes and nonmonotonic penetration trends in TF-JICF, was published in the work of Tan et al., “The regimes of twin-fluid jet-in-crossflow at atmospheric and jet-engine operating conditions,” Phy. Fluids 30, 025101 (2018). The current paper expands upon the previous report by elucidating key spray features and potential mechanisms (e.g., transitions between crossflow-driven atomization, air-driven shear-atomization, and air-driven prompt-atomization) within each TF-JICF regime, thereby providing a conceptual framework of TF-JICF for future studies.

Categories: Latest papers in fluid mechanics

### Characteristics of hydrogen jet combustion in a high-enthalpy supersonic crossflow

Physics of Fluids, Volume 31, Issue 4, April 2019.

The facilitation of a stable combustion process is of utmost importance for the realizability and performance of hypersonic propulsion systems. To elucidate the turbulent combustion characteristics, wall-modeled large eddy simulations of a transverse jet injection into a heated supersonic flow are conducted employing a detailed reaction mechanism. The computation framework utilizes an adaptive central-upwind weighted essentially nonoscillatory (WENO-CU) scheme to achieve the sixth-order accuracy in smooth flowfields, while keeping a good shock-capturing ability. The reacting zones agree well with experimental measurements in terms of the instantaneous distribution of OH radicals. And the flame penetration height has been predicted with an error of less than 17%. It is found that the turbulent reacting flow is dominated by nonpremixed combustion mainly taking place in the near-wall region and jet windward shear-layer. Moreover, the autoignition process, which plays a critical role in stabilizing supersonic combustion, shows to favor a fuel-lean or not very fuel-rich environment of a high enthalpy. Local scalar dissipation induced by turbulence gives rise to a rapid fuel mixing with the surrounding air. However, this effect may also lead to the decrease in local temperature.

The facilitation of a stable combustion process is of utmost importance for the realizability and performance of hypersonic propulsion systems. To elucidate the turbulent combustion characteristics, wall-modeled large eddy simulations of a transverse jet injection into a heated supersonic flow are conducted employing a detailed reaction mechanism. The computation framework utilizes an adaptive central-upwind weighted essentially nonoscillatory (WENO-CU) scheme to achieve the sixth-order accuracy in smooth flowfields, while keeping a good shock-capturing ability. The reacting zones agree well with experimental measurements in terms of the instantaneous distribution of OH radicals. And the flame penetration height has been predicted with an error of less than 17%. It is found that the turbulent reacting flow is dominated by nonpremixed combustion mainly taking place in the near-wall region and jet windward shear-layer. Moreover, the autoignition process, which plays a critical role in stabilizing supersonic combustion, shows to favor a fuel-lean or not very fuel-rich environment of a high enthalpy. Local scalar dissipation induced by turbulence gives rise to a rapid fuel mixing with the surrounding air. However, this effect may also lead to the decrease in local temperature.

Categories: Latest papers in fluid mechanics

### A posteriori tests of subgrid-scale models in an isothermal turbulent channel flow

Physics of Fluids, Volume 31, Issue 4, April 2019.

This paper studies the large-eddy simulation (LES) of isothermal turbulent channel flows. We investigate zero-equation algebraic models without wall function or wall model: functional models, structural models, and mixed models. In addition to models from the literature, new models are proposed and their relevance is examined. Dynamic versions of each type of model are also analyzed. The performance of the subgrid-scale models is assessed using the same finite difference numerical method and physical configuration. The friction Reynolds number of the simulations is 180. Three different mesh resolutions are used. The predictions of large-eddy simulations are compared to those of a direct numerical simulation filtered at the resolution of the LES meshes. The results are more accurate than those of a simulation without model. The predictions of functional eddy-viscosity models can be improved using constant-parameter or dynamic tensorial methods.

This paper studies the large-eddy simulation (LES) of isothermal turbulent channel flows. We investigate zero-equation algebraic models without wall function or wall model: functional models, structural models, and mixed models. In addition to models from the literature, new models are proposed and their relevance is examined. Dynamic versions of each type of model are also analyzed. The performance of the subgrid-scale models is assessed using the same finite difference numerical method and physical configuration. The friction Reynolds number of the simulations is 180. Three different mesh resolutions are used. The predictions of large-eddy simulations are compared to those of a direct numerical simulation filtered at the resolution of the LES meshes. The results are more accurate than those of a simulation without model. The predictions of functional eddy-viscosity models can be improved using constant-parameter or dynamic tensorial methods.

Categories: Latest papers in fluid mechanics

### Three-dimensional flow structures in X-shaped junctions: Effect of the Reynolds number and crossing angle

Physics of Fluids, Volume 31, Issue 4, April 2019.

We study numerically the three-dimensional (3D) dynamics of two facing flows in an X-shaped junction of two circular channels crossing at an angle α. The distribution of the fluids in the junction and in the outlet channels is determined as a function of α and the Reynolds number Re. Our goal is to describe the different flow regimes in the junction and their dependence on α and Re. We also explore to which extent two-dimensional (2D) simulations are able to describe the flow within a 3D geometry. In the 3D case, at large Re’s (≳50) and α’s (≳60°), axial vorticity (i.e., parallel to the outlet axis) of magnitude increasing both with α and Re develops in the outlet channels and cannot be reproduced by 2D numerical simulations. At lower angles (α ≲ 60°), instead, a mean vorticity component perpendicular to the junction plane is present: both its magnitude and the number of the corresponding vortices (i.e., recirculation zones) increase as α decreases. These vortices appear in both 2D and 3D simulations but at different threshold values of α and Re. At very low Re’s (≲5) and α’s (∼15°), the flow structure in 3D simulations is nearly 2D but its quantitative characteristics differ from 2D simulations. As Re increases, this two-dimensionality disappears, while vortices due to flow separation appear in the outlet channels.

We study numerically the three-dimensional (3D) dynamics of two facing flows in an X-shaped junction of two circular channels crossing at an angle α. The distribution of the fluids in the junction and in the outlet channels is determined as a function of α and the Reynolds number Re. Our goal is to describe the different flow regimes in the junction and their dependence on α and Re. We also explore to which extent two-dimensional (2D) simulations are able to describe the flow within a 3D geometry. In the 3D case, at large Re’s (≳50) and α’s (≳60°), axial vorticity (i.e., parallel to the outlet axis) of magnitude increasing both with α and Re develops in the outlet channels and cannot be reproduced by 2D numerical simulations. At lower angles (α ≲ 60°), instead, a mean vorticity component perpendicular to the junction plane is present: both its magnitude and the number of the corresponding vortices (i.e., recirculation zones) increase as α decreases. These vortices appear in both 2D and 3D simulations but at different threshold values of α and Re. At very low Re’s (≲5) and α’s (∼15°), the flow structure in 3D simulations is nearly 2D but its quantitative characteristics differ from 2D simulations. As Re increases, this two-dimensionality disappears, while vortices due to flow separation appear in the outlet channels.

Categories: Latest papers in fluid mechanics

### Analysis of rolling friction effects on oblique rebound by redefining tangential restitution and friction

Physics of Fluids, Volume 31, Issue 4, April 2019.

The planar oblique impact of a homogeneous sphere on an infinitely massive rough plane is described assuming that normal and tangential restitution mechanisms operate independently of friction, and that frictional effects include not only the usual Coulomb model but also rolling friction effects. This formulation extends early models including rolling friction effects in the description of impact events to include the independent friction restitution closure. The model yields velocity-independent equations for postimpact linear and angular velocities in four impact regimes, namely, sliding plus rolling, sliding nonrolling, stick plus rolling, and stick nonrolling whose predictions are compared with experimental data from the literature.

The planar oblique impact of a homogeneous sphere on an infinitely massive rough plane is described assuming that normal and tangential restitution mechanisms operate independently of friction, and that frictional effects include not only the usual Coulomb model but also rolling friction effects. This formulation extends early models including rolling friction effects in the description of impact events to include the independent friction restitution closure. The model yields velocity-independent equations for postimpact linear and angular velocities in four impact regimes, namely, sliding plus rolling, sliding nonrolling, stick plus rolling, and stick nonrolling whose predictions are compared with experimental data from the literature.

Categories: Latest papers in fluid mechanics

### Theoretical and numerical study on high frequency vibrational convection: Influence of the vibration direction on the flow structure

Physics of Fluids, Volume 31, Issue 4, April 2019.

Thermal convection induced simultaneously by horizontal temperature gradient and vibration in a rectangular cavity filled with molten silicon is investigated numerically and theoretically. The time averaged equations of convection are solved in the high-frequency vibration approximation. The Chebyshev spectral collocation method and a Newton-type method based on the Frechet derivative are used in the numerical solution of the streamfunction formulation of the incompressible Navier-Stokes equations. Validation by comparison with previous studies has been performed. Different values of the Grashof number Gr and vibrational Grashof number Grv and all the possible orientations of the vibrations are considered. Numerical results show that depending on the vibration direction, the flow can be amplified or damped, with even the possibility of flow inversion which can occur between critical vibration angles α1 and α2. A general theoretical expression is derived relating these critical angles and the ratio of vibrational to buoyant convection parameters, Grv/Gr. A very good agreement between the theoretical and numerical results is obtained.

Thermal convection induced simultaneously by horizontal temperature gradient and vibration in a rectangular cavity filled with molten silicon is investigated numerically and theoretically. The time averaged equations of convection are solved in the high-frequency vibration approximation. The Chebyshev spectral collocation method and a Newton-type method based on the Frechet derivative are used in the numerical solution of the streamfunction formulation of the incompressible Navier-Stokes equations. Validation by comparison with previous studies has been performed. Different values of the Grashof number Gr and vibrational Grashof number Grv and all the possible orientations of the vibrations are considered. Numerical results show that depending on the vibration direction, the flow can be amplified or damped, with even the possibility of flow inversion which can occur between critical vibration angles α1 and α2. A general theoretical expression is derived relating these critical angles and the ratio of vibrational to buoyant convection parameters, Grv/Gr. A very good agreement between the theoretical and numerical results is obtained.

Categories: Latest papers in fluid mechanics

### The effect of fluid shear on oscillating bubbly flows

Physics of Fluids, Volume 31, Issue 4, April 2019.

The impact of fluid shear on the bubble distribution in channel flows with periodically oscillating pressure gradient is examined by direct numerical simulations. Equal-sized and nearly circular bubbles are placed randomly in the channel at the initial time. In the absence of shear, the bubbles form columns spanning the width of the channel, but a strong enough shear breaks up the columns, leading to a more random bubble distribution. The effect of the nondimensional shear rate on the flow can be divided into low shear rate, moderate shear rate, and high shear rate regimes. The flow dynamics is also influenced by the Reynolds and the Euler number, and when these numbers decrease, the low shear rate regime, with stable tilted columns of bubbles, becomes smaller. Comparison of results for two- and three-dimensional flows shows that the dynamics observed in two-dimensional flows is also found in three dimensions.

The impact of fluid shear on the bubble distribution in channel flows with periodically oscillating pressure gradient is examined by direct numerical simulations. Equal-sized and nearly circular bubbles are placed randomly in the channel at the initial time. In the absence of shear, the bubbles form columns spanning the width of the channel, but a strong enough shear breaks up the columns, leading to a more random bubble distribution. The effect of the nondimensional shear rate on the flow can be divided into low shear rate, moderate shear rate, and high shear rate regimes. The flow dynamics is also influenced by the Reynolds and the Euler number, and when these numbers decrease, the low shear rate regime, with stable tilted columns of bubbles, becomes smaller. Comparison of results for two- and three-dimensional flows shows that the dynamics observed in two-dimensional flows is also found in three dimensions.

Categories: Latest papers in fluid mechanics

### Characterizing deviation from equilibrium in direct simulation Monte Carlo simulations

Physics of Fluids, Volume 31, Issue 4, April 2019.

A fundamental and yet computationally feasible parameter based on the characteristic function of the velocity distribution function (VDF) is proposed for determining the deviation from near-equilibrium conditions in rarefied flow simulations using the direct simulation Monte Carlo (DSMC) method. The proposed parameter utilizes the one-to-one correspondence between the VDF and its characteristic function (or Fourier transform), thereby correlating the deviation of the VDF (from a Chapman-Enskog VDF) with the deviation of the characteristic function (also from that of a Chapman-Enskog VDF). The results are first presented for an unsteady Bobylev solution for approach to equilibrium in 0-D, free-molecular Fourier-Couette flow problem and the Mott-Smith solution for the shock wave all of which have analytical solutions for the VDF, thereby confirming that the proposed parameter indeed captures the deviation from near-equilibrium conditions accurately. The utility of the proposed parameter is then demonstrated using two benchmark problems—Couette flow (over a range of Knudsen numbers) and structure of a normal shock (for upstream Mach numbers of 1.5, 3, and 5)—solved using the DSMC method. While the current work only presents results for benchmark one-dimensional DSMC simulations, the approach can be extended easily to rarefied flows in higher dimensions. Therefore, the proposed parameter has the potential to be used for understanding the nature of VDF and its deviation from near-equilibrium conditions at all locations in a flow field without the need for explicitly sampling the VDF.

A fundamental and yet computationally feasible parameter based on the characteristic function of the velocity distribution function (VDF) is proposed for determining the deviation from near-equilibrium conditions in rarefied flow simulations using the direct simulation Monte Carlo (DSMC) method. The proposed parameter utilizes the one-to-one correspondence between the VDF and its characteristic function (or Fourier transform), thereby correlating the deviation of the VDF (from a Chapman-Enskog VDF) with the deviation of the characteristic function (also from that of a Chapman-Enskog VDF). The results are first presented for an unsteady Bobylev solution for approach to equilibrium in 0-D, free-molecular Fourier-Couette flow problem and the Mott-Smith solution for the shock wave all of which have analytical solutions for the VDF, thereby confirming that the proposed parameter indeed captures the deviation from near-equilibrium conditions accurately. The utility of the proposed parameter is then demonstrated using two benchmark problems—Couette flow (over a range of Knudsen numbers) and structure of a normal shock (for upstream Mach numbers of 1.5, 3, and 5)—solved using the DSMC method. While the current work only presents results for benchmark one-dimensional DSMC simulations, the approach can be extended easily to rarefied flows in higher dimensions. Therefore, the proposed parameter has the potential to be used for understanding the nature of VDF and its deviation from near-equilibrium conditions at all locations in a flow field without the need for explicitly sampling the VDF.

Categories: Latest papers in fluid mechanics

### Role of Jakob number in Leidenfrost phenomena unveiled by theoretical modeling

Physics of Fluids, Volume 31, Issue 4, April 2019.

The Leidenfrost phenomenon in its most common form is encountered when a droplet is levitated and driven by its own vapor. The recently discovered “cold Leidenfrost phenomenon” expands this phenomenon into low-temperature regimes. Although various theoretical models have been proposed, analytical exploration on generalized dimensionless laws is still absent. In this work, we elucidated the role of the dimensionless Jakob number in the Leidenfrost phenomenon through theoretical modeling. The model was verified by examining the cold Leidenfrost phenomenon of both a dry ice nub on the surface of water and a liquid nitrogen droplet on a smooth silicon surface. Regardless of the specific configuration, the dimensionless temperature distribution in the vapor film only depends on the Jakob number of the vapor and presents linear dependence when the Jakob number is below 0.25. This theoretical model would facilitate the exploration of physics for Leidenfrost events and, therefore, guide prediction as well as the design of applications in the future.

The Leidenfrost phenomenon in its most common form is encountered when a droplet is levitated and driven by its own vapor. The recently discovered “cold Leidenfrost phenomenon” expands this phenomenon into low-temperature regimes. Although various theoretical models have been proposed, analytical exploration on generalized dimensionless laws is still absent. In this work, we elucidated the role of the dimensionless Jakob number in the Leidenfrost phenomenon through theoretical modeling. The model was verified by examining the cold Leidenfrost phenomenon of both a dry ice nub on the surface of water and a liquid nitrogen droplet on a smooth silicon surface. Regardless of the specific configuration, the dimensionless temperature distribution in the vapor film only depends on the Jakob number of the vapor and presents linear dependence when the Jakob number is below 0.25. This theoretical model would facilitate the exploration of physics for Leidenfrost events and, therefore, guide prediction as well as the design of applications in the future.

Categories: Latest papers in fluid mechanics

### Radial planetary vorticity tilting in the leading-edge vortex of revolving wings

Physics of Fluids, Volume 31, Issue 4, April 2019.

Previous studies suggested that Coriolis acceleration and spanwise flow both played key roles in stabilizing the leading-edge vortex (LEV) in revolving wings. The current study examined a mechanism that relates the effects of Coriolis acceleration, spanwise flow, and the tilting of the planetary vorticity on removing the radial component of LEV vorticity. Specifically, the fluid particles moving with the spanwise flow toward the wing tip are expected to experience tangential Coriolis acceleration in the wing-fixed rotating frame; therefore, a vertical gradient in spanwise flow can create a vertical gradient in the Coriolis acceleration, which will in turn produce oppositely signed radial vorticity within the LEV. This gradient of Coriolis acceleration corresponds to the radial component of planetary vorticity tilting (PVTr) that reorients the planetary vorticity into the spanwise (radial) direction, therefore producing oppositely signed radial vorticity. Using an in-house, immersed-boundary-method flow solver, this mechanism was investigated alongside the other vorticity dynamics for revolving wings of varying aspect ratio (AR = 3, 5, and 7) and Reynolds number (Re = 110 and 1400). Analyses of vorticity dynamics showed that the PVTr consistently produced oppositely signed vorticity for all values of AR and Re investigated, although other three-dimensional phenomena play a similar but more dominant role when Re = 1400. In addition, the relative strength of the PVTr increased with increasing AR due to a decrease in the magnitude of advection. Finally, a dimensional analysis was performed on the advection and PVTr for the different AR and Re.

Previous studies suggested that Coriolis acceleration and spanwise flow both played key roles in stabilizing the leading-edge vortex (LEV) in revolving wings. The current study examined a mechanism that relates the effects of Coriolis acceleration, spanwise flow, and the tilting of the planetary vorticity on removing the radial component of LEV vorticity. Specifically, the fluid particles moving with the spanwise flow toward the wing tip are expected to experience tangential Coriolis acceleration in the wing-fixed rotating frame; therefore, a vertical gradient in spanwise flow can create a vertical gradient in the Coriolis acceleration, which will in turn produce oppositely signed radial vorticity within the LEV. This gradient of Coriolis acceleration corresponds to the radial component of planetary vorticity tilting (PVTr) that reorients the planetary vorticity into the spanwise (radial) direction, therefore producing oppositely signed radial vorticity. Using an in-house, immersed-boundary-method flow solver, this mechanism was investigated alongside the other vorticity dynamics for revolving wings of varying aspect ratio (AR = 3, 5, and 7) and Reynolds number (Re = 110 and 1400). Analyses of vorticity dynamics showed that the PVTr consistently produced oppositely signed vorticity for all values of AR and Re investigated, although other three-dimensional phenomena play a similar but more dominant role when Re = 1400. In addition, the relative strength of the PVTr increased with increasing AR due to a decrease in the magnitude of advection. Finally, a dimensional analysis was performed on the advection and PVTr for the different AR and Re.

Categories: Latest papers in fluid mechanics

### Control of vortex-induced vibration of a circular cylinder using a pair of air jets at low Reynolds number

Physics of Fluids, Volume 31, Issue 4, April 2019.

A numerical investigation was conducted to assess the effectiveness of an active control method using a pair of air jets positioned at the two shoulders of a circular cylinder for vortex-induced vibration (VIV) suppression at a low Reynolds number of 100. Unlike the same-phase jet-control technique, air injection leads to gas-liquid two-phase flow in the wake of cylinder. The ejected air is wrapped by the shear layer, and an air vortex is generated after the curled jet flow attains a certain length, corresponding to the consumption of ejecting energy. Then, air bubbles are formed and convected downstream with the shed vortices. The air vortices and bubbles interrupt the development of boundary layer and naturally shedding vortices, effectively delaying the vortex formation and hence the VIV suppression. The migration of air bubbles in the flow wake are categorized into two modes. One is bubbles coinciding with vortices and convecting downstream with them. The other is bubbles deviating from the center of vortices but continually interrupting the vortices by drawing the ambient vorticity-carrying fluid. The vibration control becomes more effective with the increase of momentum coefficient. After implementing air-jet control at Ujet/Uin = 2, more than 60% reduction in transverse amplitude is achieved.

A numerical investigation was conducted to assess the effectiveness of an active control method using a pair of air jets positioned at the two shoulders of a circular cylinder for vortex-induced vibration (VIV) suppression at a low Reynolds number of 100. Unlike the same-phase jet-control technique, air injection leads to gas-liquid two-phase flow in the wake of cylinder. The ejected air is wrapped by the shear layer, and an air vortex is generated after the curled jet flow attains a certain length, corresponding to the consumption of ejecting energy. Then, air bubbles are formed and convected downstream with the shed vortices. The air vortices and bubbles interrupt the development of boundary layer and naturally shedding vortices, effectively delaying the vortex formation and hence the VIV suppression. The migration of air bubbles in the flow wake are categorized into two modes. One is bubbles coinciding with vortices and convecting downstream with them. The other is bubbles deviating from the center of vortices but continually interrupting the vortices by drawing the ambient vorticity-carrying fluid. The vibration control becomes more effective with the increase of momentum coefficient. After implementing air-jet control at Ujet/Uin = 2, more than 60% reduction in transverse amplitude is achieved.

Categories: Latest papers in fluid mechanics

### The boundary layer flow induced above the torsional motion of a disk

Physics of Fluids, Volume 31, Issue 4, April 2019.

The boundary layer flow above a disk in torsional motion with azimuthal velocity proportional to rm is investigated for all values of m ≥ 1; here, r is the radial coordinate measured from the center of the disk. The resulting flow is a fully three-dimensional exact solution to the steady, axisymmetric boundary layer equations in the form of similarity solutions. We compute wall shear stresses in the radial and azimuthal directions as a function of the torsional exponent m, as well as the flow induced in the far field. The large m asymptotics of the problem are computed and compared with numerical solutions. The induced radial velocity profiles have a “wall-jet” structure, and it is found that both the radial and azimuthal velocity components become confined close to the surface of the disk as m increases.

The boundary layer flow above a disk in torsional motion with azimuthal velocity proportional to rm is investigated for all values of m ≥ 1; here, r is the radial coordinate measured from the center of the disk. The resulting flow is a fully three-dimensional exact solution to the steady, axisymmetric boundary layer equations in the form of similarity solutions. We compute wall shear stresses in the radial and azimuthal directions as a function of the torsional exponent m, as well as the flow induced in the far field. The large m asymptotics of the problem are computed and compared with numerical solutions. The induced radial velocity profiles have a “wall-jet” structure, and it is found that both the radial and azimuthal velocity components become confined close to the surface of the disk as m increases.

Categories: Latest papers in fluid mechanics