# 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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### Comment on “A periodic grain consolidation model of porous media” [Phys. Fluids A 1, 38 (1989)]

Physics of Fluids, Volume 31, Issue 10, October 2019.

In this document, we correct the friction coefficient values presented in Table III in a study by Larson and Higdon [“A periodic grain consolidation model of porous media,” Phys. Fluids A 1, 38 (1989)]. The authors addressed the problem of Stokes flow through periodic arrays of (non)overlapping spheres and determined the friction coefficients. It appears that the volume of the overlapping region of spheres was not taken into account, which affected the total solid concentration and systematically biased the corresponding friction coefficient values. We correct the sphere concentration and friction coefficients, and validate our approach with lattice-Boltzmann simulations. The suggested correction is valid in the case of overlapping spheres only, when the volume of the overlapping region is positive.

In this document, we correct the friction coefficient values presented in Table III in a study by Larson and Higdon [“A periodic grain consolidation model of porous media,” Phys. Fluids A 1, 38 (1989)]. The authors addressed the problem of Stokes flow through periodic arrays of (non)overlapping spheres and determined the friction coefficients. It appears that the volume of the overlapping region of spheres was not taken into account, which affected the total solid concentration and systematically biased the corresponding friction coefficient values. We correct the sphere concentration and friction coefficients, and validate our approach with lattice-Boltzmann simulations. The suggested correction is valid in the case of overlapping spheres only, when the volume of the overlapping region is positive.

Categories: Latest papers in fluid mechanics

### Dynamic Leidenfrost behaviors of different fluid drops on superheated surface: Scaling for vapor film thickness

Physics of Fluids, Volume 31, Issue 10, October 2019.

For an impact drop on a superheated surface, the dynamic Leidenfrost temperature, TLF, depends on several parameters such as impact velocity, vapor layer thickness, and thermophysical properties of the fluids. In this letter, we derived a scaling formula for TLF using the well-known balance relation between the pressures exerted by drop impact and evaporated vapor flow. As the TLF scale intrinsically requires estimating the vapor film thickness δv, it should be scaled based on the consideration of relevant physics postulated on the impact drop and evaporated vapor. Thus, for proper scaling of δv, we considered the drop–vapor interface deformation by drop inertial and surface tension forces during initial impact of drop. Results showed that δv could be scaled with drop diameter D0 and Weber number We. For drops with low We (<10), δv scaled to ∼D0We−1/4 and ∼D0We−2/5 for drops with higher We. The explicit scale for TLF agreed well with present experimental data.

For an impact drop on a superheated surface, the dynamic Leidenfrost temperature, TLF, depends on several parameters such as impact velocity, vapor layer thickness, and thermophysical properties of the fluids. In this letter, we derived a scaling formula for TLF using the well-known balance relation between the pressures exerted by drop impact and evaporated vapor flow. As the TLF scale intrinsically requires estimating the vapor film thickness δv, it should be scaled based on the consideration of relevant physics postulated on the impact drop and evaporated vapor. Thus, for proper scaling of δv, we considered the drop–vapor interface deformation by drop inertial and surface tension forces during initial impact of drop. Results showed that δv could be scaled with drop diameter D0 and Weber number We. For drops with low We (<10), δv scaled to ∼D0We−1/4 and ∼D0We−2/5 for drops with higher We. The explicit scale for TLF agreed well with present experimental data.

Categories: Latest papers in fluid mechanics

### Bi-global stability analysis in curvilinear coordinates

Physics of Fluids, Volume 31, Issue 10, October 2019.

A method is developed to solve biglobal stability functions in curvilinear systems which avoids reshaping of the airfoil or remapping the disturbance flow fields. As well, the biglobal stability functions for calculation in a curvilinear system are derived. The instability features of the flow over a NACA (National Advisory Committee for Aeronautics) 0025 airfoil at two different angles of attack, corresponding to a flow with a separation bubble and a fully separated flow, are investigated at a chord-based Reynolds number of 100 000. The most unstable mode was found to be related to the wake instability, with a dimensionless frequency close to one. For the flow with a separation bubble, there is an instability plateau in the dimensionless frequency ranging from 2 to 5.5. After the plateau and for an increasing dimensionless frequency, the growth rate of the most unstable mode decreases. For a fully separated flow, the plateau is narrower than that for the flow with a separation bubble. After the plateau, with an increased dimensionless frequency, the growth rate of the most unstable mode decreases and then increases once again. The growth rate of the upstream shear layer instability was found to be larger than that of the downstream shear layer instability.

A method is developed to solve biglobal stability functions in curvilinear systems which avoids reshaping of the airfoil or remapping the disturbance flow fields. As well, the biglobal stability functions for calculation in a curvilinear system are derived. The instability features of the flow over a NACA (National Advisory Committee for Aeronautics) 0025 airfoil at two different angles of attack, corresponding to a flow with a separation bubble and a fully separated flow, are investigated at a chord-based Reynolds number of 100 000. The most unstable mode was found to be related to the wake instability, with a dimensionless frequency close to one. For the flow with a separation bubble, there is an instability plateau in the dimensionless frequency ranging from 2 to 5.5. After the plateau and for an increasing dimensionless frequency, the growth rate of the most unstable mode decreases. For a fully separated flow, the plateau is narrower than that for the flow with a separation bubble. After the plateau, with an increased dimensionless frequency, the growth rate of the most unstable mode decreases and then increases once again. The growth rate of the upstream shear layer instability was found to be larger than that of the downstream shear layer instability.

Categories: Latest papers in fluid mechanics

### Asymmetric vortexes induced traveling drop on an oscillatory liquid bath

Physics of Fluids, Volume 31, Issue 10, October 2019.

The traveling and dancing behaviors of the bouncing drops on the oscillating liquid bath have been reported in several investigations. It was shown that the normal force during the impact of the drop on an inclined liquid surface is responsible for the traveling of a 0.8 mm-sized drop. Here, we report that a pair of vortexes can be induced by the repeated impact of a 2 mm-sized drop on an oscillatory liquid bath. The traveling of a large drop on the oscillatory liquid bath with an inclined bottom is found to be associated with the induced asymmetric vortex flow underneath the liquid surface. The effect of the vortex flow becomes significant for the size of a drop larger than 1.8 mm. Two-coupled drops with different sizes are found to be self-propelled on the oscillatory liquid bath with a flat bottom. The coupled drops propagate toward the direction of the small-sized drop. The distribution of the vortex flow is investigated by the particle image velocimetry (PIV) technique and the numerical simulation of the acoustic streaming model. PIV measurement and numerical simulation of the speed distribution of the vortex flows induced by the single bouncing drop and two-coupled drops show consistent results. It is suspected that the traveling of two-coupled drops is associated with the motion of the small drop and the liquid flow near the liquid surface.

The traveling and dancing behaviors of the bouncing drops on the oscillating liquid bath have been reported in several investigations. It was shown that the normal force during the impact of the drop on an inclined liquid surface is responsible for the traveling of a 0.8 mm-sized drop. Here, we report that a pair of vortexes can be induced by the repeated impact of a 2 mm-sized drop on an oscillatory liquid bath. The traveling of a large drop on the oscillatory liquid bath with an inclined bottom is found to be associated with the induced asymmetric vortex flow underneath the liquid surface. The effect of the vortex flow becomes significant for the size of a drop larger than 1.8 mm. Two-coupled drops with different sizes are found to be self-propelled on the oscillatory liquid bath with a flat bottom. The coupled drops propagate toward the direction of the small-sized drop. The distribution of the vortex flow is investigated by the particle image velocimetry (PIV) technique and the numerical simulation of the acoustic streaming model. PIV measurement and numerical simulation of the speed distribution of the vortex flows induced by the single bouncing drop and two-coupled drops show consistent results. It is suspected that the traveling of two-coupled drops is associated with the motion of the small drop and the liquid flow near the liquid surface.

Categories: Latest papers in fluid mechanics

### Air-water meniscus shape in superhydrophobic triangular microgroove is dictated by a critical pressure under dynamic conditions

Physics of Fluids, Volume 31, Issue 10, October 2019.

We bring out a critical force for shape transition of air-water meniscus in superhydrophobic triangular microgrooves under dynamic conditions, considering an intricate interplay of the viscous and capillary forces. A closed form theoretical expression for the critical force depicts its explicit dependence on the groove geometry and relevant physical properties. A negative value of this critical force denotes a convex meniscus shape, whereas a positive value signifies a concave meniscus shape. Considering the shape transition, the critical pressure is further interpreted to denote a physical condition under which the meniscus is nontrivially flat, despite the existence of surface tension forces. Our analysis opens up a paradigm by which the meniscus shape in a groove can be virtually controlled at will, consistent with the specific requirements such as drag reduction, as demanded by the application on hand.

We bring out a critical force for shape transition of air-water meniscus in superhydrophobic triangular microgrooves under dynamic conditions, considering an intricate interplay of the viscous and capillary forces. A closed form theoretical expression for the critical force depicts its explicit dependence on the groove geometry and relevant physical properties. A negative value of this critical force denotes a convex meniscus shape, whereas a positive value signifies a concave meniscus shape. Considering the shape transition, the critical pressure is further interpreted to denote a physical condition under which the meniscus is nontrivially flat, despite the existence of surface tension forces. Our analysis opens up a paradigm by which the meniscus shape in a groove can be virtually controlled at will, consistent with the specific requirements such as drag reduction, as demanded by the application on hand.

Categories: Latest papers in fluid mechanics

### The jet characteristics of bubbles near mixed boundaries

Physics of Fluids, Volume 31, Issue 10, October 2019.

The jet characteristics of bubbles near mixed boundaries have been the focus of research in many fields. As the associated parameters are complicated, relatively few reports have been published. In this paper, a numerical model is established by considering the influence of the free surface and a mutual vertical wall using the boundary element method. To determine the jet characteristics of collapsing bubbles in different areas, two nondimensional parameters must be investigated: the distance γv from the bubble to the vertical wall and the distance γh from the bubble to the horizontal wall. At the same time, the buoyancy parameter δ cannot be ignored. First, the jet characteristics under an infinite vertical solid wall are discussed; furthermore, the jet direction in the stage of collapsing bubble under combined boundaries without buoyancy is studied, and we find that the variation amplitude of the jet angle changes with the free surface. Considering the buoyancy, we then divide the total area into six regions with different ranges of jet angle under small buoyancy values, allowing the significant effect of buoyancy to be studied as δ increases. In addition, we study the jet velocity qualitatively under the condition of negligible buoyancy and find that a peak jet velocity may exist at mid water depths.

The jet characteristics of bubbles near mixed boundaries have been the focus of research in many fields. As the associated parameters are complicated, relatively few reports have been published. In this paper, a numerical model is established by considering the influence of the free surface and a mutual vertical wall using the boundary element method. To determine the jet characteristics of collapsing bubbles in different areas, two nondimensional parameters must be investigated: the distance γv from the bubble to the vertical wall and the distance γh from the bubble to the horizontal wall. At the same time, the buoyancy parameter δ cannot be ignored. First, the jet characteristics under an infinite vertical solid wall are discussed; furthermore, the jet direction in the stage of collapsing bubble under combined boundaries without buoyancy is studied, and we find that the variation amplitude of the jet angle changes with the free surface. Considering the buoyancy, we then divide the total area into six regions with different ranges of jet angle under small buoyancy values, allowing the significant effect of buoyancy to be studied as δ increases. In addition, we study the jet velocity qualitatively under the condition of negligible buoyancy and find that a peak jet velocity may exist at mid water depths.

Categories: Latest papers in fluid mechanics

### An investigation for influence of intense thermal convection events on wall turbulence in the near-neutral atmospheric surface layer

Physics of Fluids, Volume 31, Issue 10, October 2019.

Based on the field observation data in the near-neutral atmospheric surface layer (ASL) at the Qingtu Lake Observation Array, a new experimental data processing of the second-order statistic distribution of the high Reynolds number wall turbulence was presented which considered the influence of the intense thermal convection events (ITCEs). Following the conventional data selection in the literature, i.e., |z/L|, it is known that the variation of the large- and/or the very-large-scale motions (LSMs and VLSMs) cannot be effectively performed only by this method, which motivates us to find other factors influencing these turbulent motions, e.g., the ITCEs. From the data analysis of the probability density distribution of vertical heat flux, it is found that although its mean value tends to zero, its variance is large rather than zero, which suggests to us some ITCEs exist in the natural motions, although it has less frequent occurrences. In order to characterize the effect of such ITCEs, an additional parameter ψ for scaling the ratio of the buoyancy force to the viscous force is proposed in the data selection progress. The results show that the greater the |ψ|, the greater the impact of the ITCEs on ASL wall turbulence. Furthermore, our investigation reveals that the ITCEs may be one of the reasons why the VLSMs exhibit the Top-Down mechanism.

Based on the field observation data in the near-neutral atmospheric surface layer (ASL) at the Qingtu Lake Observation Array, a new experimental data processing of the second-order statistic distribution of the high Reynolds number wall turbulence was presented which considered the influence of the intense thermal convection events (ITCEs). Following the conventional data selection in the literature, i.e., |z/L|, it is known that the variation of the large- and/or the very-large-scale motions (LSMs and VLSMs) cannot be effectively performed only by this method, which motivates us to find other factors influencing these turbulent motions, e.g., the ITCEs. From the data analysis of the probability density distribution of vertical heat flux, it is found that although its mean value tends to zero, its variance is large rather than zero, which suggests to us some ITCEs exist in the natural motions, although it has less frequent occurrences. In order to characterize the effect of such ITCEs, an additional parameter ψ for scaling the ratio of the buoyancy force to the viscous force is proposed in the data selection progress. The results show that the greater the |ψ|, the greater the impact of the ITCEs on ASL wall turbulence. Furthermore, our investigation reveals that the ITCEs may be one of the reasons why the VLSMs exhibit the Top-Down mechanism.

Categories: Latest papers in fluid mechanics

### Quasi-classical trajectory-based non-equilibrium chemical reaction models for hypersonic air flows

Physics of Fluids, Volume 31, Issue 10, October 2019.

Phenomenological models, such as Park’s widely used two temperature model, overpredict the reaction rate coefficients at vibrationally cold conditions and underpredict it at vibrationally hot conditions. To this end, two new chemical reaction models, the nonequilibrium total temperature (NETT) and nonequilibrium piecewise interpolation models for the continuum framework are presented. The focus is on matching the reaction rate coefficients calculated using a quasiclassical trajectory based dissociation cross section database. The NETT model is an intuitive model based on physical understanding of the reaction at a molecular level. A new nonequilibrium parameter and the use of total temperature in the exponential term of the Arrhenius fit ensure the NETT model has a simple and straightforward implementation. The efficacy of the new model was investigated for several equilibrium and nonequilibrium conditions in the form of heat bath simulations. Additionally, two-dimensional hypersonic flows around a flat blunt-body were simulated by employing various chemical reaction models to validate the new models using experimental shock tube data. Park’s two temperature model predicted higher dissociation rates and a higher degree of dissociation leading to lower peak vibrational temperatures compared to those predicted by the new nonequilibrium models. Overall, the present work demonstrates that the new nonequilibrium models perform better than Park’s two temperature model, especially in simulations with a high degree of nonequilibrium, particularly as observed in re-entry flows.

Phenomenological models, such as Park’s widely used two temperature model, overpredict the reaction rate coefficients at vibrationally cold conditions and underpredict it at vibrationally hot conditions. To this end, two new chemical reaction models, the nonequilibrium total temperature (NETT) and nonequilibrium piecewise interpolation models for the continuum framework are presented. The focus is on matching the reaction rate coefficients calculated using a quasiclassical trajectory based dissociation cross section database. The NETT model is an intuitive model based on physical understanding of the reaction at a molecular level. A new nonequilibrium parameter and the use of total temperature in the exponential term of the Arrhenius fit ensure the NETT model has a simple and straightforward implementation. The efficacy of the new model was investigated for several equilibrium and nonequilibrium conditions in the form of heat bath simulations. Additionally, two-dimensional hypersonic flows around a flat blunt-body were simulated by employing various chemical reaction models to validate the new models using experimental shock tube data. Park’s two temperature model predicted higher dissociation rates and a higher degree of dissociation leading to lower peak vibrational temperatures compared to those predicted by the new nonequilibrium models. Overall, the present work demonstrates that the new nonequilibrium models perform better than Park’s two temperature model, especially in simulations with a high degree of nonequilibrium, particularly as observed in re-entry flows.

Categories: Latest papers in fluid mechanics

### Effects of upstream pipe length on pipe-cavity jet noise

Physics of Fluids, Volume 31, Issue 10, October 2019.

An experimental study is carried out to quantify the acoustic radiation of underexpanded pipe-cavity jet noise. Pipe-cavity configurations with different upstream pipe lengths are studied over a range of Mach numbers. Detailed acoustic measurements such as frequency analysis, sound pressure levels, directivity, and acoustic power analysis are carried out to show the effect of upstream pipe length. Finite element simulations are carried to predict the resonance frequencies of the pipe-cavity. Results of simulation with zero mean flow condition match well with theoretical results and the present experiments. The far-field acoustic spectrum exhibits strong cavity tones and shock associated noise. The results show that the pipe-cavity resonates close to the combined tangential-longitudinal mode. The increase in shear layer thickness tends to attenuate the cavity tones, with a small increase in screech tonal noise. An increase in upstream pipe length leads to a decrease in overall sound pressure levels and acoustic power.

An experimental study is carried out to quantify the acoustic radiation of underexpanded pipe-cavity jet noise. Pipe-cavity configurations with different upstream pipe lengths are studied over a range of Mach numbers. Detailed acoustic measurements such as frequency analysis, sound pressure levels, directivity, and acoustic power analysis are carried out to show the effect of upstream pipe length. Finite element simulations are carried to predict the resonance frequencies of the pipe-cavity. Results of simulation with zero mean flow condition match well with theoretical results and the present experiments. The far-field acoustic spectrum exhibits strong cavity tones and shock associated noise. The results show that the pipe-cavity resonates close to the combined tangential-longitudinal mode. The increase in shear layer thickness tends to attenuate the cavity tones, with a small increase in screech tonal noise. An increase in upstream pipe length leads to a decrease in overall sound pressure levels and acoustic power.

Categories: Latest papers in fluid mechanics

### Effect of electrostatic forces on the distribution of drops in turbulent channel flows

Physics of Fluids, Volume 31, Issue 10, October 2019.

The effect of electrostatic forces on the distribution of drops in turbulent channel flows is examined by direct numerical simulations. The droplets and suspending fluid are assumed to be leaky dielectric fluids. We set the electrical conductivity ratio (R = σi/σo) smaller than the dielectric permittivity ratio (S−1 = εi/εo) to drive the flow from the drop poles to their equators. The results show that an applied external electric field has a significant effect on the microstructure and the flow properties. For flows without an electric field, where the Mason (Mn) number is infinity, the drops aggregated in the core of the channel and the liquid streamwise velocity are similar to those in single-phase flow. For Mn = 0.1, a low electric intensity, most of the drops are driven to the walls due to the unbalanced electric force on the drop interface. For Mn = 0.05, drops are more likely to stick together because of the stronger combination of electrohydrodynamic effect and dielectrophoretic force between drops. Therefore, the number of drops in the middle of the channel increases while still many drops are in the wall layer. For Mn = 0.007, the electric intensity is very strong and all the drops in the channel tend to line up and form columns spanning the channel width. These columns become unstable when the flow drives them close to each other. It is also found that an increase of the electric intensity can lead to an increase in the average wall shear stress. In addition, the liquid streamwise velocity will become more uniform, which means the effective viscosity of the system is increased, when Mn = 0.007.

The effect of electrostatic forces on the distribution of drops in turbulent channel flows is examined by direct numerical simulations. The droplets and suspending fluid are assumed to be leaky dielectric fluids. We set the electrical conductivity ratio (R = σi/σo) smaller than the dielectric permittivity ratio (S−1 = εi/εo) to drive the flow from the drop poles to their equators. The results show that an applied external electric field has a significant effect on the microstructure and the flow properties. For flows without an electric field, where the Mason (Mn) number is infinity, the drops aggregated in the core of the channel and the liquid streamwise velocity are similar to those in single-phase flow. For Mn = 0.1, a low electric intensity, most of the drops are driven to the walls due to the unbalanced electric force on the drop interface. For Mn = 0.05, drops are more likely to stick together because of the stronger combination of electrohydrodynamic effect and dielectrophoretic force between drops. Therefore, the number of drops in the middle of the channel increases while still many drops are in the wall layer. For Mn = 0.007, the electric intensity is very strong and all the drops in the channel tend to line up and form columns spanning the channel width. These columns become unstable when the flow drives them close to each other. It is also found that an increase of the electric intensity can lead to an increase in the average wall shear stress. In addition, the liquid streamwise velocity will become more uniform, which means the effective viscosity of the system is increased, when Mn = 0.007.

Categories: Latest papers in fluid mechanics

### Inertial effects in triple-layer core-annular pipeline flow

Physics of Fluids, Volume 31, Issue 10, October 2019.

Triple-layer core-annular flow is a novel methodology for efficient heavy oil transportation. As usual, high shear rates concentrating in a lubricating fluid layer reduce the pressure drop significantly. Novel is the use of a viscoplastic fluid bounding the lubricant and protecting the transported core. For sufficiently large yield stress, the skin remains unyielded, preventing any interfacial instabilities. By shaping the skin, we generate lubrication forces to counterbalance buoyancy of the core fluid, i.e., an eccentric position of the core is the result of buoyancy and lubrication forces balancing. Here, we extend the feasibility of this method to large pipes and higher flow rates by considering the effects of inertia and turbulence in the lubrication layer. We show that the method can generate enough lubrication force to balance the buoyancy force for a wide range of density differences and pipe sizes if the proper shape is imposed on the unyielded skin.

Triple-layer core-annular flow is a novel methodology for efficient heavy oil transportation. As usual, high shear rates concentrating in a lubricating fluid layer reduce the pressure drop significantly. Novel is the use of a viscoplastic fluid bounding the lubricant and protecting the transported core. For sufficiently large yield stress, the skin remains unyielded, preventing any interfacial instabilities. By shaping the skin, we generate lubrication forces to counterbalance buoyancy of the core fluid, i.e., an eccentric position of the core is the result of buoyancy and lubrication forces balancing. Here, we extend the feasibility of this method to large pipes and higher flow rates by considering the effects of inertia and turbulence in the lubrication layer. We show that the method can generate enough lubrication force to balance the buoyancy force for a wide range of density differences and pipe sizes if the proper shape is imposed on the unyielded skin.

Categories: Latest papers in fluid mechanics

### Notable effect of the subgrid-scale stress anisotropy on mean-velocity prediction through budget of the grid-scale Reynolds-shear stress

Physics of Fluids, Volume 31, Issue 10, October 2019.

In large eddy simulation (LES), the mean-velocity distribution in wall turbulence depends strongly on the distribution of the ensemble-averaged Reynolds (Re) shear stress, which consists of two parts: the resolved grid-scale (GS) and unresolved subgrid-scale (SGS) components. As the grid resolution becomes coarser, the GS component decreases and thus the SGS component must increase to compensate for this. The GS decrease is originally caused by filtering, through which the power spectrum is cut off mainly in the high-wavenumber region. Therefore, the SGS model has been discussed mostly in terms of the energy transfer between the GS and SGS components. Recently, however, some studies have found that the SGS-stress anisotropy directly influences instantaneous GS vortex motions. This also means that the SGS stress may have a large effect on the ensemble-averaged GS Re stress because the instantaneous fluctuation of the SGS stress correlates with that of the velocity gradient in the GS budget. In this study, we investigate in detail the effect of the SGS stress on predicting the resolved GS Re shear stress through its budget. For this purpose, we perform a priori tests with highly resolved LES data of a plane channel flow. The knowledge obtained is then confirmed by a posteriori tests for various grid resolutions and Reynolds numbers. It is found that the SGS-stress anisotropy is very important for providing a reasonable trend of the GS Re shear stress, leading to more accurate prediction of the mean velocity for coarse-grid resolutions.

In large eddy simulation (LES), the mean-velocity distribution in wall turbulence depends strongly on the distribution of the ensemble-averaged Reynolds (Re) shear stress, which consists of two parts: the resolved grid-scale (GS) and unresolved subgrid-scale (SGS) components. As the grid resolution becomes coarser, the GS component decreases and thus the SGS component must increase to compensate for this. The GS decrease is originally caused by filtering, through which the power spectrum is cut off mainly in the high-wavenumber region. Therefore, the SGS model has been discussed mostly in terms of the energy transfer between the GS and SGS components. Recently, however, some studies have found that the SGS-stress anisotropy directly influences instantaneous GS vortex motions. This also means that the SGS stress may have a large effect on the ensemble-averaged GS Re stress because the instantaneous fluctuation of the SGS stress correlates with that of the velocity gradient in the GS budget. In this study, we investigate in detail the effect of the SGS stress on predicting the resolved GS Re shear stress through its budget. For this purpose, we perform a priori tests with highly resolved LES data of a plane channel flow. The knowledge obtained is then confirmed by a posteriori tests for various grid resolutions and Reynolds numbers. It is found that the SGS-stress anisotropy is very important for providing a reasonable trend of the GS Re shear stress, leading to more accurate prediction of the mean velocity for coarse-grid resolutions.

Categories: Latest papers in fluid mechanics

### Application of two-branch deep neural network to predict bubble migration near elastic boundaries

Physics of Fluids, Volume 31, Issue 10, October 2019.

Compared to the drawbacks of traditional experimental and numerical methods for predicting bubble migration, such as high experimental costs and complex simulation operations, the data-driven approach of using deep neural network algorithms can provide an alternative method. The objective of this paper is to construct a two-branch deep neural network (TBDNN) model in order to improve the high-fidelity bubble migration results and further reduce dependence on the quantity of experimental data. A TBDNN model is obtained by embedding the features of the Kelvin impulse into a basic deep neural network (BDNN) system. The results show that compared to the original BDNN model, TBDNN performs much better in accurately predicting bubble migration based on the same amount of training data. Using the TBDNN model, the critical condition of bubble oscillation at a fixed location can be detected under the influence of boundary properties (normalized stiffness and mass) and bubble standoff. Furthermore, the initial position of the bubble and normalized stiffness of boundaries have a positive correlation with bubble migration, whereas normalized mass has a negative impact. It was found that the normalized mass of boundaries plays the most important role in affecting bubble migration compared to the standoff and stiffness when using the method of variable sensitivity analysis.

Compared to the drawbacks of traditional experimental and numerical methods for predicting bubble migration, such as high experimental costs and complex simulation operations, the data-driven approach of using deep neural network algorithms can provide an alternative method. The objective of this paper is to construct a two-branch deep neural network (TBDNN) model in order to improve the high-fidelity bubble migration results and further reduce dependence on the quantity of experimental data. A TBDNN model is obtained by embedding the features of the Kelvin impulse into a basic deep neural network (BDNN) system. The results show that compared to the original BDNN model, TBDNN performs much better in accurately predicting bubble migration based on the same amount of training data. Using the TBDNN model, the critical condition of bubble oscillation at a fixed location can be detected under the influence of boundary properties (normalized stiffness and mass) and bubble standoff. Furthermore, the initial position of the bubble and normalized stiffness of boundaries have a positive correlation with bubble migration, whereas normalized mass has a negative impact. It was found that the normalized mass of boundaries plays the most important role in affecting bubble migration compared to the standoff and stiffness when using the method of variable sensitivity analysis.

Categories: Latest papers in fluid mechanics

### Erratum: “The stabilization of a hypersonic boundary layer using local sections of porous coating” [Phys. Fluids 24, 034105 (2012)]

Physics of Fluids, Volume 31, Issue 10, October 2019.

Categories: Latest papers in fluid mechanics

### Erratum: “Analysis of the flow of a thin liquid film on the surface of a rotating, curved, axisymmetric substrate” [Phys. Fluids 30, 082110 (2018)]

Physics of Fluids, Volume 31, Issue 10, October 2019.

Categories: Latest papers in fluid mechanics

### Flow boiling heat transfer in silicon microgaps with multiple hotspots and variable pin fin clustering

Physics of Fluids, Volume MNFC2019, Issue 1, October 2019.

Microfluidic interlayer cooling has been demonstrated as a practical solution for the vertical stacking of high power microelectronics. Although a considerable amount of studies has been presented for single phase cooling with this approach, the flow boiling features in more complex arrangements have not been as thoroughly studied. The embedded cooling of microelectronics is feasible with the use of dielectric refrigerants, which are ideally used in two-phase conditions in order to exploit the latent heat of vaporization. In the present investigation, the two-phase cooling in silicon microgaps is assessed under variable power and heat transfer surface area densities. The dielectric refrigerant HFE-7200 is used as the working fluid under flow boiling conditions, analyzing useful characteristics such as the two-phase flow regime, heat transfer, and pressure drop. The present investigation uses a numerical model that is capable of predicting the relevant features of flow boiling phenomena through a mechanistic phase-change model. The results from this study demonstrate that multiple hotspots with variable pin densities can be effectively controlled, with relatively uniform temperatures, under flow boiling conditions with dielectric fluids.

Microfluidic interlayer cooling has been demonstrated as a practical solution for the vertical stacking of high power microelectronics. Although a considerable amount of studies has been presented for single phase cooling with this approach, the flow boiling features in more complex arrangements have not been as thoroughly studied. The embedded cooling of microelectronics is feasible with the use of dielectric refrigerants, which are ideally used in two-phase conditions in order to exploit the latent heat of vaporization. In the present investigation, the two-phase cooling in silicon microgaps is assessed under variable power and heat transfer surface area densities. The dielectric refrigerant HFE-7200 is used as the working fluid under flow boiling conditions, analyzing useful characteristics such as the two-phase flow regime, heat transfer, and pressure drop. The present investigation uses a numerical model that is capable of predicting the relevant features of flow boiling phenomena through a mechanistic phase-change model. The results from this study demonstrate that multiple hotspots with variable pin densities can be effectively controlled, with relatively uniform temperatures, under flow boiling conditions with dielectric fluids.

Categories: Latest papers in fluid mechanics

### Flow boiling heat transfer in silicon microgaps with multiple hotspots and variable pin fin clustering

Physics of Fluids, Volume 31, Issue 10, October 2019.

Microfluidic interlayer cooling has been demonstrated as a practical solution for the vertical stacking of high power microelectronics. Although a considerable amount of studies has been presented for single phase cooling with this approach, the flow boiling features in more complex arrangements have not been as thoroughly studied. The embedded cooling of microelectronics is feasible with the use of dielectric refrigerants, which are ideally used in two-phase conditions in order to exploit the latent heat of vaporization. In the present investigation, the two-phase cooling in silicon microgaps is assessed under variable power and heat transfer surface area densities. The dielectric refrigerant HFE-7200 is used as the working fluid under flow boiling conditions, analyzing useful characteristics such as the two-phase flow regime, heat transfer, and pressure drop. The present investigation uses a numerical model that is capable of predicting the relevant features of flow boiling phenomena through a mechanistic phase-change model. The results from this study demonstrate that multiple hotspots with variable pin densities can be effectively controlled, with relatively uniform temperatures, under flow boiling conditions with dielectric fluids.

Microfluidic interlayer cooling has been demonstrated as a practical solution for the vertical stacking of high power microelectronics. Although a considerable amount of studies has been presented for single phase cooling with this approach, the flow boiling features in more complex arrangements have not been as thoroughly studied. The embedded cooling of microelectronics is feasible with the use of dielectric refrigerants, which are ideally used in two-phase conditions in order to exploit the latent heat of vaporization. In the present investigation, the two-phase cooling in silicon microgaps is assessed under variable power and heat transfer surface area densities. The dielectric refrigerant HFE-7200 is used as the working fluid under flow boiling conditions, analyzing useful characteristics such as the two-phase flow regime, heat transfer, and pressure drop. The present investigation uses a numerical model that is capable of predicting the relevant features of flow boiling phenomena through a mechanistic phase-change model. The results from this study demonstrate that multiple hotspots with variable pin densities can be effectively controlled, with relatively uniform temperatures, under flow boiling conditions with dielectric fluids.

Categories: Latest papers in fluid mechanics

### On the peripheral intensification of two-dimensional vortices in smaller-scale randomly forcing flow

Physics of Fluids, Volume 31, Issue 10, October 2019.

The evolution of a monopolar vortex embedded in the field of smaller-scale randomly forced vorticity is examined using fully nonlinear two-dimensional simulations at large Reynolds numbers. The vortex is considered to be compact if its angular momentum decreases with the radius on the scale comparable to the radius of maximum azimuthal velocity. The energy decays without forcing, while the vortex remains compact despite its viscous spreading. This scenario dramatically changes in the strong forcing regime, characterized by the substantial growth of the vortex energy due to the increase in velocity and angular momentum at the vortex periphery so that ultimately, the vortex transforms into a noncompact structure. The maximum of angular momentum redistribution is found to be proportional to the enstrophy of smaller-scale vorticity field. The results have important implications for better understanding the fate of vortices and physical mechanisms of energy transfer.

The evolution of a monopolar vortex embedded in the field of smaller-scale randomly forced vorticity is examined using fully nonlinear two-dimensional simulations at large Reynolds numbers. The vortex is considered to be compact if its angular momentum decreases with the radius on the scale comparable to the radius of maximum azimuthal velocity. The energy decays without forcing, while the vortex remains compact despite its viscous spreading. This scenario dramatically changes in the strong forcing regime, characterized by the substantial growth of the vortex energy due to the increase in velocity and angular momentum at the vortex periphery so that ultimately, the vortex transforms into a noncompact structure. The maximum of angular momentum redistribution is found to be proportional to the enstrophy of smaller-scale vorticity field. The results have important implications for better understanding the fate of vortices and physical mechanisms of energy transfer.

Categories: Latest papers in fluid mechanics

### Study on flow separation and transition of the airfoil in low Reynolds number

Physics of Fluids, Volume 31, Issue 10, October 2019.

As typical flow characteristics in a low Reynolds number, laminar separation bubbles (LSBs) and transition to turbulence over airfoils have been extensively studied in recent years. In order to analyze their flow mechanism, numerical investigation using the finite volume method to solve the Reynolds averaged Navier-Stokes equations with a transition Shear Stress Transport (SST) four-equation transition model is performed in this work, combined with the experimental study facilitated by the oil film interferometry technique. Specifically, the transition SST four-equation transition model is solved to simulate the separation location and LSB structure at low Reynolds numbers on a Wortmann FX63-137 airfoil. Good agreement is obtained between the numerical simulation and experimental measurements regarding the separation, transition and reattachment location, aerodynamic coefficients, and overall flow structures. At higher Reynolds numbers of 200 000 and 300 000, similar bubble structures on the airfoil surface are observed, and the location of the bubble moves toward the leading edge of the airfoil by increasing the angle of attack. However, in Reynolds numbers ranging from 300 000 to 500 000, significant changes of the laminar flow separation structures emerge. The flow structure changes from the classical laminar separation bubble to the nonclassical separation flow structure that is composed of a major vortex 1(V1) and a minor vortex 2(V2). Due to the small distance between V1 and V2, it is difficult to distinguish the delicate structure of the two separation bubbles from the classical laminar separation bubble by the experimental method.

As typical flow characteristics in a low Reynolds number, laminar separation bubbles (LSBs) and transition to turbulence over airfoils have been extensively studied in recent years. In order to analyze their flow mechanism, numerical investigation using the finite volume method to solve the Reynolds averaged Navier-Stokes equations with a transition Shear Stress Transport (SST) four-equation transition model is performed in this work, combined with the experimental study facilitated by the oil film interferometry technique. Specifically, the transition SST four-equation transition model is solved to simulate the separation location and LSB structure at low Reynolds numbers on a Wortmann FX63-137 airfoil. Good agreement is obtained between the numerical simulation and experimental measurements regarding the separation, transition and reattachment location, aerodynamic coefficients, and overall flow structures. At higher Reynolds numbers of 200 000 and 300 000, similar bubble structures on the airfoil surface are observed, and the location of the bubble moves toward the leading edge of the airfoil by increasing the angle of attack. However, in Reynolds numbers ranging from 300 000 to 500 000, significant changes of the laminar flow separation structures emerge. The flow structure changes from the classical laminar separation bubble to the nonclassical separation flow structure that is composed of a major vortex 1(V1) and a minor vortex 2(V2). Due to the small distance between V1 and V2, it is difficult to distinguish the delicate structure of the two separation bubbles from the classical laminar separation bubble by the experimental method.

Categories: Latest papers in fluid mechanics

### Finite obstacle effect on the aerodynamic performance of a hovering wing

Physics of Fluids, Volume 31, Issue 10, October 2019.

The finite obstacle effect on the aerodynamic performance of a normal hovering wing is studied using the immersed boundary method. Phenomena of a two-dimensional wing hovering above, under, or on the side of a circular obstacle are presented. Parameters including obstacle size, distance, location, and flapping angle are investigated to study how the aerodynamic force and flow field are affected. The diameter of the obstacle ranges from 0.5c to 12c and the distance between the centroid of the wing and obstacle surface from 0.5c to 6c (c is the wing chord length). Previous observations of ground effects including force enhancement, reduction, and recovery occur similarly when the wing hovers above the obstacle of diameter greater than 2c. However, finite obstacles affect the aerodynamic performance differently when the size shrinks to a critical value. Force drops when the wing moves close and rises when moving away, opposite to the ground effect. As flapping angle amplitude increases, the force change tends to be consistent for different-sized obstacles. The top or side effect shows a different influence on the force change. Force monotonically increases as the distance decreases when the wing hovers under the obstacle. The side effect places a less important factor on the aerodynamic performance. All force changes under such circumstance are less than 13% referring to nonobstacle result. The gap between the leading or trailing edge of the wing and obstacle surface plays a significant role in the leading and trailing edge vortices generating, shedding, and pairing, which greatly affects the force change.

The finite obstacle effect on the aerodynamic performance of a normal hovering wing is studied using the immersed boundary method. Phenomena of a two-dimensional wing hovering above, under, or on the side of a circular obstacle are presented. Parameters including obstacle size, distance, location, and flapping angle are investigated to study how the aerodynamic force and flow field are affected. The diameter of the obstacle ranges from 0.5c to 12c and the distance between the centroid of the wing and obstacle surface from 0.5c to 6c (c is the wing chord length). Previous observations of ground effects including force enhancement, reduction, and recovery occur similarly when the wing hovers above the obstacle of diameter greater than 2c. However, finite obstacles affect the aerodynamic performance differently when the size shrinks to a critical value. Force drops when the wing moves close and rises when moving away, opposite to the ground effect. As flapping angle amplitude increases, the force change tends to be consistent for different-sized obstacles. The top or side effect shows a different influence on the force change. Force monotonically increases as the distance decreases when the wing hovers under the obstacle. The side effect places a less important factor on the aerodynamic performance. All force changes under such circumstance are less than 13% referring to nonobstacle result. The gap between the leading or trailing edge of the wing and obstacle surface plays a significant role in the leading and trailing edge vortices generating, shedding, and pairing, which greatly affects the force change.

Categories: Latest papers in fluid mechanics