# Latest papers in fluid mechanics

### Floating of solid non-magnetic bodies in magnetic fluids: Comprehensive analysis in the framework of inductive approach

Physics of Fluids, Volume 32, Issue 11, November 2020.

This paper presents a study of the ponderomotive force acting on a solid non-magnetic sphere immersed in a magnetic fluid cylindrical container magnetized by an external homogeneous magnetic field. The problem has been studied experimentally, numerically, and analytically. The analytical study was carried out in the framework of the inductive approach, which made it possible to take into account the demagnetizing fields generated by both the magnetic fluid and the non-magnetic body. All methods of investigation used in this work showed the same non-standard force behavior with two extrema. The existence of the non-monotonous force is explained by the competition between two mechanisms: the inhomogeneous demagnetizing field inside the cylindrical container and the interaction of the solid body dipole with its own mirror image. The results of numerical simulations are in quantitative agreement with the experimental data, and the analytical results are in qualitative agreement with the experimental data.

This paper presents a study of the ponderomotive force acting on a solid non-magnetic sphere immersed in a magnetic fluid cylindrical container magnetized by an external homogeneous magnetic field. The problem has been studied experimentally, numerically, and analytically. The analytical study was carried out in the framework of the inductive approach, which made it possible to take into account the demagnetizing fields generated by both the magnetic fluid and the non-magnetic body. All methods of investigation used in this work showed the same non-standard force behavior with two extrema. The existence of the non-monotonous force is explained by the competition between two mechanisms: the inhomogeneous demagnetizing field inside the cylindrical container and the interaction of the solid body dipole with its own mirror image. The results of numerical simulations are in quantitative agreement with the experimental data, and the analytical results are in qualitative agreement with the experimental data.

Categories: Latest papers in fluid mechanics

### Relative entropy based breakdown criteria for hybrid discrete velocity Bhatnagar–Gross–Krook and lattice Boltzmann method

Physics of Fluids, Volume 32, Issue 11, November 2020.

In the present paper, novel breakdown criteria for the assessment of the validity of the continuum-fluid approximation are proposed. The approach is based on relative entropy (Kullback–Leibler divergence). The considered variants of the Kullback–Leibler divergence assess the contribution of non-hydrodynamic components of the gas velocity distribution function to the overall entropy. In addition, the chi-square statistic is introduced as a breakdown variable. As benchmark problems, the plane Couette and force driven Poiseuille flows are considered for various Knudsen and Mach numbers. The modeling is performed with the difference scheme for the kinetic Bhatnagar–Gross–Krook equation and the hybrid approach: the Bhatnagar–Gross–Krook equation is applied in non-equilibrium regions, and the lattice Boltzmann method is applied as the continuum-fluid method. The simulation results show that the proposed criteria can efficiently separate equilibrium and non-equilibrium domains.

In the present paper, novel breakdown criteria for the assessment of the validity of the continuum-fluid approximation are proposed. The approach is based on relative entropy (Kullback–Leibler divergence). The considered variants of the Kullback–Leibler divergence assess the contribution of non-hydrodynamic components of the gas velocity distribution function to the overall entropy. In addition, the chi-square statistic is introduced as a breakdown variable. As benchmark problems, the plane Couette and force driven Poiseuille flows are considered for various Knudsen and Mach numbers. The modeling is performed with the difference scheme for the kinetic Bhatnagar–Gross–Krook equation and the hybrid approach: the Bhatnagar–Gross–Krook equation is applied in non-equilibrium regions, and the lattice Boltzmann method is applied as the continuum-fluid method. The simulation results show that the proposed criteria can efficiently separate equilibrium and non-equilibrium domains.

Categories: Latest papers in fluid mechanics

### Experimental investigation of the separation of binary gaseous mixtures flowing through a capillary tube

Physics of Fluids, Volume 32, Issue 11, November 2020.

This paper presents an optical method to investigate the separation phenomenon for the flow of a near-equimolar mixture of carbon dioxide and helium through a hollow-core photonic crystal fiber using tunable diode laser absorption spectroscopy to measure the temporal evolution of the path-integrated absorption of carbon dioxide. The gas flow was initiated by a pressure difference between two gas cells, each connected to one end of the fiber under isothermal conditions. The change in path-integrated concentration of CO2 over time was used to infer the separation of the gases, defined as the dimensionless quantity Φ in this paper. To investigate the effects of pressure ratio and rarefaction on the separation phenomenon, these parameters were varied in the experiments. The separation Φ increases from zero with no pressure gradient, reaching an asymptotic maximum value for pressure ratios exceeding 20. To examine the effect of rarefaction on Φ, measurements have been conducted for the binary mixture flowing into near-vacuum, covering a range of inlet Knudsen numbers (Kn) between 0.016 and 2. The separation Φ increases with Kn for 0.01 < Kn < 0.1, reaching a peak value at Kn ≈ 0.1, and then decreases with a further increase in Kn. This effect has not previously been noted in the literature. The experimental results are compared with a numerical model, demonstrating good agreement. Based on these findings, we have summarized the necessary conditions for carbon dioxide/helium separation to occur inside a capillary tube, which can be used as a mechanism for small-scale gas separation applications.

This paper presents an optical method to investigate the separation phenomenon for the flow of a near-equimolar mixture of carbon dioxide and helium through a hollow-core photonic crystal fiber using tunable diode laser absorption spectroscopy to measure the temporal evolution of the path-integrated absorption of carbon dioxide. The gas flow was initiated by a pressure difference between two gas cells, each connected to one end of the fiber under isothermal conditions. The change in path-integrated concentration of CO2 over time was used to infer the separation of the gases, defined as the dimensionless quantity Φ in this paper. To investigate the effects of pressure ratio and rarefaction on the separation phenomenon, these parameters were varied in the experiments. The separation Φ increases from zero with no pressure gradient, reaching an asymptotic maximum value for pressure ratios exceeding 20. To examine the effect of rarefaction on Φ, measurements have been conducted for the binary mixture flowing into near-vacuum, covering a range of inlet Knudsen numbers (Kn) between 0.016 and 2. The separation Φ increases with Kn for 0.01 < Kn < 0.1, reaching a peak value at Kn ≈ 0.1, and then decreases with a further increase in Kn. This effect has not previously been noted in the literature. The experimental results are compared with a numerical model, demonstrating good agreement. Based on these findings, we have summarized the necessary conditions for carbon dioxide/helium separation to occur inside a capillary tube, which can be used as a mechanism for small-scale gas separation applications.

Categories: Latest papers in fluid mechanics

### Two-stage growth mode for lift-off mechanism in oblique shock-wave/jet interaction

Physics of Fluids, Volume 32, Issue 11, November 2020.

The lift-off flow of the supersonic streamwise vortex in oblique shock-wave/jet interaction (OS/JI), extracted from a wall-mounted ramp injector in the scramjet, is studied through the large-eddy simulation method. The shocked helium jet deforms into a pair of the streamwise vortex with a co-rotating companion vortex. The trajectory of the streamwise vortex center is lifted by the shock interaction. Based on the objective coordinate system in the frame of oblique shock, it is found that the nature of the three-dimensional lift-off structure of the OS/JI is inherently and precisely controlled by the structure kinetics of a corresponding shock bubble interaction (SBI). The striking similarities of both qualitative and quantitative results between the OS/JI and the SBI support the proposition that the lift-off of the streamwise vortex is the result of an underlying two-dimensional vortical motion. By combining the first-stage linear growth mode of Richtmyer–Meshkov instability with the second-stage vortex formation mode, a two-stage vortex propagation model suitable for the SBI is proposed and validated. The lift-off growth of a shocked jet in the OS/JI concerned and in the wall-mounted ramp injector cases from the literature is well explained under the two-stage vortex propagation model of SBI. This model further predicts that increasing ramp compression shows little effect on elevating the streamwise vortex for higher free-stream Mach numbers (Ma > 5). In comparison, evident lift-off may occur for lower Mach numbers (Ma < 3.5), which offers the new way for the preliminary design of a streamwise vortex-based ramp injector in the scramjet.

The lift-off flow of the supersonic streamwise vortex in oblique shock-wave/jet interaction (OS/JI), extracted from a wall-mounted ramp injector in the scramjet, is studied through the large-eddy simulation method. The shocked helium jet deforms into a pair of the streamwise vortex with a co-rotating companion vortex. The trajectory of the streamwise vortex center is lifted by the shock interaction. Based on the objective coordinate system in the frame of oblique shock, it is found that the nature of the three-dimensional lift-off structure of the OS/JI is inherently and precisely controlled by the structure kinetics of a corresponding shock bubble interaction (SBI). The striking similarities of both qualitative and quantitative results between the OS/JI and the SBI support the proposition that the lift-off of the streamwise vortex is the result of an underlying two-dimensional vortical motion. By combining the first-stage linear growth mode of Richtmyer–Meshkov instability with the second-stage vortex formation mode, a two-stage vortex propagation model suitable for the SBI is proposed and validated. The lift-off growth of a shocked jet in the OS/JI concerned and in the wall-mounted ramp injector cases from the literature is well explained under the two-stage vortex propagation model of SBI. This model further predicts that increasing ramp compression shows little effect on elevating the streamwise vortex for higher free-stream Mach numbers (Ma > 5). In comparison, evident lift-off may occur for lower Mach numbers (Ma < 3.5), which offers the new way for the preliminary design of a streamwise vortex-based ramp injector in the scramjet.

Categories: Latest papers in fluid mechanics

### Shear-induced dispersion in peristaltic flow

Physics of Fluids, Volume 32, Issue 11, November 2020.

The effective diffusivity of a Brownian tracer in unidirectional flow is well known to be enhanced due to shear by the classic phenomenon of Taylor dispersion. At long times, the average concentration of the tracer follows a simplified advection–diffusion equation with an effective shear-dependent dispersivity. In this work, we make use of the generalized Taylor dispersion theory for periodic domains to analyze tracer dispersion by peristaltic pumping. In channels with small aspect ratios, asymptotic expansions in the lubrication limit are employed to obtain analytical expressions for the dispersion coefficient at both small and high Péclet numbers. Channels of arbitrary aspect ratios are also considered using a boundary integral formulation for the fluid flow coupled to a conservation equation for the effective dispersivity, which is solved using the finite-volume method. Our theoretical calculations, which compare well with results from Brownian dynamics simulations, elucidate the effects of channel geometry and pumping strength on shear-induced dispersion. We further discuss the connection between the present problem and dispersion due to Taylor’s swimming sheet and interpret our results in the purely diffusive regime in the context of Fick–Jacobs theory. Our results provide the theoretical basis for understanding passive scalar transport in peristaltic flow, for instance, in the ureter or in microfluidic peristaltic pumps.

The effective diffusivity of a Brownian tracer in unidirectional flow is well known to be enhanced due to shear by the classic phenomenon of Taylor dispersion. At long times, the average concentration of the tracer follows a simplified advection–diffusion equation with an effective shear-dependent dispersivity. In this work, we make use of the generalized Taylor dispersion theory for periodic domains to analyze tracer dispersion by peristaltic pumping. In channels with small aspect ratios, asymptotic expansions in the lubrication limit are employed to obtain analytical expressions for the dispersion coefficient at both small and high Péclet numbers. Channels of arbitrary aspect ratios are also considered using a boundary integral formulation for the fluid flow coupled to a conservation equation for the effective dispersivity, which is solved using the finite-volume method. Our theoretical calculations, which compare well with results from Brownian dynamics simulations, elucidate the effects of channel geometry and pumping strength on shear-induced dispersion. We further discuss the connection between the present problem and dispersion due to Taylor’s swimming sheet and interpret our results in the purely diffusive regime in the context of Fick–Jacobs theory. Our results provide the theoretical basis for understanding passive scalar transport in peristaltic flow, for instance, in the ureter or in microfluidic peristaltic pumps.

Categories: Latest papers in fluid mechanics

### Shock-wave thickness influence to the light diffraction on a plane shock wave

Physics of Fluids, Volume 32, Issue 11, November 2020.

This study is devoted to the numerical analysis of the result of light distribution after passing it through a shock wave, depending on the degree of gas rarefaction. The obtained numerical results allowed reproducing the experimental shadowgraph images obtained in our study. The range of shock wave thickness (from 0 mm to 20 mm) allowed considering the qualitative change in the light distribution on the screen during switching from the regime where the wave nature of light has the greatest influence on the distribution of light to the regime of the geometric optics approach. As a result, the criteria for the applicability of the shadowgraphy technique for the experimental description of the shock wave internal structure were obtained.

This study is devoted to the numerical analysis of the result of light distribution after passing it through a shock wave, depending on the degree of gas rarefaction. The obtained numerical results allowed reproducing the experimental shadowgraph images obtained in our study. The range of shock wave thickness (from 0 mm to 20 mm) allowed considering the qualitative change in the light distribution on the screen during switching from the regime where the wave nature of light has the greatest influence on the distribution of light to the regime of the geometric optics approach. As a result, the criteria for the applicability of the shadowgraphy technique for the experimental description of the shock wave internal structure were obtained.

Categories: Latest papers in fluid mechanics

### Effect of pulsating injection and mainstream attack angle on film cooling performance of a gas turbine blade

Physics of Fluids, Volume 32, Issue 11, November 2020.

Relatively few studies have examined the effects of pulsating unsteadiness in turbine cooling blades. This unsteadiness can be a result of compressor blades and vane interaction. In addition, there is a particular lack of data of full turbine blades at various angles of attack. The effects of pulsation frequency (f = 2 Hz, 50 Hz, and 100 Hz) and the angle of attack (α = 0°, 15°, and 30°) on the film cooling effectiveness of a row film jet at the leading edge of a modified NASA C3X blade for two blowing ratios (M = 0.5 and 1.0) in comparison with the steady state experimentally investigated on pressure and suction sides of the blade and the flow field are obtained by simulation. Three-dimensional transient Reynolds-averaged Navier–Stokes equations coupled with the shear stress transport turbulence model (SST k − ω) are used in this research. Square waves are considered to pulse the injection air. Results show that the distribution of the instantaneous film cooling effectiveness is affected by frequency, angle of attack, blowing ratio, and curvature of the blade. With an increase in the angle of attack and the pulsing frequency, the averaged film cooling effectiveness increased. Pulsation and angle of attack have different effects on the performance of the injection jet toward the pressure and suction sides of the blade. Mixing of injection air with the mainstream at the pressure side is more than that at the suction side. Under certain conditions, the averaged film cooling effectiveness of pulsation flow is greater than the steady jet.

Relatively few studies have examined the effects of pulsating unsteadiness in turbine cooling blades. This unsteadiness can be a result of compressor blades and vane interaction. In addition, there is a particular lack of data of full turbine blades at various angles of attack. The effects of pulsation frequency (f = 2 Hz, 50 Hz, and 100 Hz) and the angle of attack (α = 0°, 15°, and 30°) on the film cooling effectiveness of a row film jet at the leading edge of a modified NASA C3X blade for two blowing ratios (M = 0.5 and 1.0) in comparison with the steady state experimentally investigated on pressure and suction sides of the blade and the flow field are obtained by simulation. Three-dimensional transient Reynolds-averaged Navier–Stokes equations coupled with the shear stress transport turbulence model (SST k − ω) are used in this research. Square waves are considered to pulse the injection air. Results show that the distribution of the instantaneous film cooling effectiveness is affected by frequency, angle of attack, blowing ratio, and curvature of the blade. With an increase in the angle of attack and the pulsing frequency, the averaged film cooling effectiveness increased. Pulsation and angle of attack have different effects on the performance of the injection jet toward the pressure and suction sides of the blade. Mixing of injection air with the mainstream at the pressure side is more than that at the suction side. Under certain conditions, the averaged film cooling effectiveness of pulsation flow is greater than the steady jet.

Categories: Latest papers in fluid mechanics

### Instability induced by wall deformability in sliding Couette flow

Physics of Fluids, Volume 32, Issue 11, November 2020.

The linear stability of “sliding Couette flow” of a Newtonian fluid through the annular gap formed by two concentric cylinders having a ratio of inner to outer cylinder radii, β, and driven by the axial motion of the inner cylinder is studied in the low Reynolds number (<1) regime. The inner wall of the outer cylinder is lined by a deformable neo-Hookean solid layer of dimensionless thickness H. This flow configuration is encountered in medical procedures such as thread-injection and angioplasty, where the inserted needle is surrounded by the deformable wall of blood vessels. In stark contrast to the configuration with rigid cylinders, we predict the existence of finite- and short-wave linear instabilities even in the creeping-flow limit, driven by the deformable nature of the outer cylinder. Interestingly, these instabilities exist for arbitrary β, and even for non-axisymmetric perturbations, in parameter regimes where the flow is stable for the configuration with a rigid outer cylinder. For the finite-wave instability, the axisymmetric mode is the most critical mode of the instability, while the non-axisymmetric mode with azimuthal wavenumber n = 4 is the critical mode for the short-wave instability. By replacing the outer rigid boundary surrounding the deformable wall by an “unrestrained” stress-free boundary, we demonstrate that the flow becomes significantly more unstable. Thus, the present study shows that sliding Couette flow with a deformable wall can be linearly unstable at an arbitrarily low Reynolds number, in direct contrast to the stability of the same configuration with a rigid cylinder.

The linear stability of “sliding Couette flow” of a Newtonian fluid through the annular gap formed by two concentric cylinders having a ratio of inner to outer cylinder radii, β, and driven by the axial motion of the inner cylinder is studied in the low Reynolds number (<1) regime. The inner wall of the outer cylinder is lined by a deformable neo-Hookean solid layer of dimensionless thickness H. This flow configuration is encountered in medical procedures such as thread-injection and angioplasty, where the inserted needle is surrounded by the deformable wall of blood vessels. In stark contrast to the configuration with rigid cylinders, we predict the existence of finite- and short-wave linear instabilities even in the creeping-flow limit, driven by the deformable nature of the outer cylinder. Interestingly, these instabilities exist for arbitrary β, and even for non-axisymmetric perturbations, in parameter regimes where the flow is stable for the configuration with a rigid outer cylinder. For the finite-wave instability, the axisymmetric mode is the most critical mode of the instability, while the non-axisymmetric mode with azimuthal wavenumber n = 4 is the critical mode for the short-wave instability. By replacing the outer rigid boundary surrounding the deformable wall by an “unrestrained” stress-free boundary, we demonstrate that the flow becomes significantly more unstable. Thus, the present study shows that sliding Couette flow with a deformable wall can be linearly unstable at an arbitrarily low Reynolds number, in direct contrast to the stability of the same configuration with a rigid cylinder.

Categories: Latest papers in fluid mechanics

### Capillary number correlations for two-phase flow in porous media

Author(s): R. Hilfer

Relative permeabilities and capillary number correlations are widely used for quantitative estimates of enhanced water flood performance in porous media. They enter as essential parameters into reservoir simulations. Experimental capillary number correlations for seven different reservoir rocks and ...

[Phys. Rev. E 102, 053103] Published Wed Nov 04, 2020

Categories: Latest papers in fluid mechanics

### Numerical analysis of Richtmyer–Meshkov instability of circular density interface in presence of transverse magnetic field

Physics of Fluids, Volume 32, Issue 11, November 2020.

Richtmyer–Meshkov instability (RMI) caused by the interaction of a shock wave and a density interface in the presence of a transverse magnetic field is investigated numerically using the ideal compressible magneto-hydro-dynamic (MHD) equations. The MHD equations are solved with the corner transport upwind + constrained transport algorithm that guarantees the divergence-free constraint on the magnetic field. The numerical results clearly capture the evolution of the density interface induced by the RMI for both HD and MHD situations, which are in good agreement with the previous experimental and numerical results. Moreover, current numerical results reveal a potential stabilizing mechanism of the flow instability by the transverse magnetic field: it is found that the magnetic tension produces a torque on the interface fluid, which is opposite to the torque driven by the velocity shear; therefore, the Kelvin–Helmholtz instability on the density interface caused by the velocity shear is effectively suppressed. In addition, detailed information about the magnetic strength, magnetic energy, magnetic tension, and vorticity on the density interface is also quantitatively analyzed, and the results suggest that the RMI is quite an efficient mechanism for the amplification of the magnetic field, which, in turn, enhances the suppression of the flow instability.

Richtmyer–Meshkov instability (RMI) caused by the interaction of a shock wave and a density interface in the presence of a transverse magnetic field is investigated numerically using the ideal compressible magneto-hydro-dynamic (MHD) equations. The MHD equations are solved with the corner transport upwind + constrained transport algorithm that guarantees the divergence-free constraint on the magnetic field. The numerical results clearly capture the evolution of the density interface induced by the RMI for both HD and MHD situations, which are in good agreement with the previous experimental and numerical results. Moreover, current numerical results reveal a potential stabilizing mechanism of the flow instability by the transverse magnetic field: it is found that the magnetic tension produces a torque on the interface fluid, which is opposite to the torque driven by the velocity shear; therefore, the Kelvin–Helmholtz instability on the density interface caused by the velocity shear is effectively suppressed. In addition, detailed information about the magnetic strength, magnetic energy, magnetic tension, and vorticity on the density interface is also quantitatively analyzed, and the results suggest that the RMI is quite an efficient mechanism for the amplification of the magnetic field, which, in turn, enhances the suppression of the flow instability.

Categories: Latest papers in fluid mechanics

### Erratum: “Improved theoretical model of two-dimensional flow field in a severely narrow circular pipe” [Phys. Fluids 31, 065107 (2019)]

Physics of Fluids, Volume 32, Issue 11, November 2020.

Categories: Latest papers in fluid mechanics

### Deconvolutional artificial neural network models for large eddy simulation of turbulence

Physics of Fluids, Volume 32, Issue 11, November 2020.

Deconvolutional artificial neural network (DANN) models are developed for subgrid-scale (SGS) stress in large eddy simulation (LES) of turbulence. The filtered velocities at different spatial points are used as input features of the DANN models to reconstruct the unfiltered velocity. The grid width of the DANN models is chosen to be smaller than the filter width in order to accurately model the effects of SGS dynamics. The DANN models can predict the SGS stress more accurately than the conventional approximate deconvolution method and velocity gradient model in the a priori study: the correlation coefficients can be made larger than 99% and the relative errors can be made less than 15% for the DANN model. In an a posteriori study, a comprehensive comparison of the DANN model, the implicit LES (ILES), the dynamic Smagorinsky model (DSM), and the dynamic mixed model (DMM) shows that the DANN model is superior to the ILES, DSM, and DMM models in the prediction of the velocity spectrum, various statistics of velocity, and the instantaneous coherent structures without increasing the considerable computational cost; the time for the DANN model to calculate the SGS stress is about 1.3 times that of the DMM model. In addition, the trained DANN models without any fine-tuning can predict the velocity statistics well for different filter widths. These results indicate that the DANN framework with the consideration of SGS spatial features is a promising approach to develop advanced SGS models in the LES of turbulence.

Deconvolutional artificial neural network (DANN) models are developed for subgrid-scale (SGS) stress in large eddy simulation (LES) of turbulence. The filtered velocities at different spatial points are used as input features of the DANN models to reconstruct the unfiltered velocity. The grid width of the DANN models is chosen to be smaller than the filter width in order to accurately model the effects of SGS dynamics. The DANN models can predict the SGS stress more accurately than the conventional approximate deconvolution method and velocity gradient model in the a priori study: the correlation coefficients can be made larger than 99% and the relative errors can be made less than 15% for the DANN model. In an a posteriori study, a comprehensive comparison of the DANN model, the implicit LES (ILES), the dynamic Smagorinsky model (DSM), and the dynamic mixed model (DMM) shows that the DANN model is superior to the ILES, DSM, and DMM models in the prediction of the velocity spectrum, various statistics of velocity, and the instantaneous coherent structures without increasing the considerable computational cost; the time for the DANN model to calculate the SGS stress is about 1.3 times that of the DMM model. In addition, the trained DANN models without any fine-tuning can predict the velocity statistics well for different filter widths. These results indicate that the DANN framework with the consideration of SGS spatial features is a promising approach to develop advanced SGS models in the LES of turbulence.

Categories: Latest papers in fluid mechanics

### On different kinetic approaches for computing planar gas expansion under pulsed evaporation into vacuum

Physics of Fluids, Volume 32, Issue 11, November 2020.

The numerical study of one-dimensional gas expansion under pulsed evaporation into vacuum is carried out on the basis of the direct simulation Monte Carlo method, the exact Boltzmann kinetic equation, and the S-model kinetic equation. The results are presented for various levels of evaporation intensity, defined by the amount of evaporated material. Special attention has been paid to the calculation of the average axial energy of particles, the velocity vector of which deviates from the axis by no more than a small prescribed angle α. This characteristic of the flow is important for analysis of time-of-flight distributions in pulsed laser ablation. It is found that for intense evaporation, the average axial energy has a maximum as a function of time. The presented results allow us to establish the relative accuracy of the considered kinetic approaches for various flow regimes.

The numerical study of one-dimensional gas expansion under pulsed evaporation into vacuum is carried out on the basis of the direct simulation Monte Carlo method, the exact Boltzmann kinetic equation, and the S-model kinetic equation. The results are presented for various levels of evaporation intensity, defined by the amount of evaporated material. Special attention has been paid to the calculation of the average axial energy of particles, the velocity vector of which deviates from the axis by no more than a small prescribed angle α. This characteristic of the flow is important for analysis of time-of-flight distributions in pulsed laser ablation. It is found that for intense evaporation, the average axial energy has a maximum as a function of time. The presented results allow us to establish the relative accuracy of the considered kinetic approaches for various flow regimes.

Categories: Latest papers in fluid mechanics

### Bistable states and separation hysteresis in curved compression ramp flows

Physics of Fluids, Volume 32, Issue 11, November 2020.

The separation hysteresis of the boundary layer induced by the variation of the angle of attack (AOA) is observed and investigated numerically in curved compression ramp (CCR) flows. The occurrence of this new phenomenon is based on the bistable states of CCR flows even for the same free-stream and boundary conditions, indicating that the boundary layer’s state (attachment/separation) depends on its evolutionary history with AOA varying. Specifically, beginning with an attachment state, the boundary layer remains attached as AOA increases slowly and suddenly separates once AOA reaches a marginal angle αs. However, if we decrease AOA back from this angle, the boundary layer will not attach and remain separated until AOA reaches a small enough angle αa. The AOA extent [αa, αs] is called the dual-solution region. Three characteristic adverse pressure gradients (APGs), Isb, Ic[math], and Ib, are proposed to explain the existence of this dual-solution region, where Ic[math] and Isb (Ic[math] < Isb) are induced by the curved wall and the separation bubble, respectively, and Ib is the maximum APG that the boundary layer can resist. (i) When Ib > Isb, the flow must be attached, (ii) when Ib < Ic[math], the flow must be separated, and (iii) when Ic[math] < Ib < Isb, both of these two states are theoretically possible. Since AOA-variation can make (i), (ii), and (iii) occur alternately, it could induce the separation hysteresis of CCR flows, which has been observed in this paper.

The separation hysteresis of the boundary layer induced by the variation of the angle of attack (AOA) is observed and investigated numerically in curved compression ramp (CCR) flows. The occurrence of this new phenomenon is based on the bistable states of CCR flows even for the same free-stream and boundary conditions, indicating that the boundary layer’s state (attachment/separation) depends on its evolutionary history with AOA varying. Specifically, beginning with an attachment state, the boundary layer remains attached as AOA increases slowly and suddenly separates once AOA reaches a marginal angle αs. However, if we decrease AOA back from this angle, the boundary layer will not attach and remain separated until AOA reaches a small enough angle αa. The AOA extent [αa, αs] is called the dual-solution region. Three characteristic adverse pressure gradients (APGs), Isb, Ic[math], and Ib, are proposed to explain the existence of this dual-solution region, where Ic[math] and Isb (Ic[math] < Isb) are induced by the curved wall and the separation bubble, respectively, and Ib is the maximum APG that the boundary layer can resist. (i) When Ib > Isb, the flow must be attached, (ii) when Ib < Ic[math], the flow must be separated, and (iii) when Ic[math] < Ib < Isb, both of these two states are theoretically possible. Since AOA-variation can make (i), (ii), and (iii) occur alternately, it could induce the separation hysteresis of CCR flows, which has been observed in this paper.

Categories: Latest papers in fluid mechanics

### Predicting the near-wall velocity of wall turbulence using a neural network for particle image velocimetry

Physics of Fluids, Volume 32, Issue 11, November 2020.

Near-wall velocity prediction for wall-bounded turbulence is useful for constructing a wall model and estimating dissipation and wall shear stress. A convolutional neural network is developed to improve the near-wall velocity prediction and spatial resolution for wall-bounded turbulent velocity fields obtained using particle image velocimetry (PIV). To establish the relationship between the low-resolution and high-resolution fields, this machine learning model is trained on a synthetic PIV dataset generated based on velocity fields obtained from the direct numerical simulation of turbulent channel flows at Reτ = 1000. Using a test dataset with a higher Reynolds number of Reτ = 5200, the performance of this model is assessed in terms of instantaneous fields, error analysis, velocity statistics, and energy spectra. The influences of the interrogation window, image resolution, and particle concentration on the performance of this network are also considered. We further apply this network to practical PIV data from a turbulent boundary layer at Reτ = 2200 to assess the network performance under real experimental conditions. The results indicate that the proposed machine-learning-based model can predict missing near-wall velocity fields and enhance the spatial resolution of PIV fields, but the accuracy for Reynolds shear stress prediction needs to be further improved. The presented approach shows the potential ability to predict the near-wall instantaneous velocity of high-Reynolds-number turbulence from low-Reynolds-number flow fields.

Near-wall velocity prediction for wall-bounded turbulence is useful for constructing a wall model and estimating dissipation and wall shear stress. A convolutional neural network is developed to improve the near-wall velocity prediction and spatial resolution for wall-bounded turbulent velocity fields obtained using particle image velocimetry (PIV). To establish the relationship between the low-resolution and high-resolution fields, this machine learning model is trained on a synthetic PIV dataset generated based on velocity fields obtained from the direct numerical simulation of turbulent channel flows at Reτ = 1000. Using a test dataset with a higher Reynolds number of Reτ = 5200, the performance of this model is assessed in terms of instantaneous fields, error analysis, velocity statistics, and energy spectra. The influences of the interrogation window, image resolution, and particle concentration on the performance of this network are also considered. We further apply this network to practical PIV data from a turbulent boundary layer at Reτ = 2200 to assess the network performance under real experimental conditions. The results indicate that the proposed machine-learning-based model can predict missing near-wall velocity fields and enhance the spatial resolution of PIV fields, but the accuracy for Reynolds shear stress prediction needs to be further improved. The presented approach shows the potential ability to predict the near-wall instantaneous velocity of high-Reynolds-number turbulence from low-Reynolds-number flow fields.

Categories: Latest papers in fluid mechanics

### Compressible lattice Boltzmann methods with adaptive velocity stencils: An interpolation-free formulation

Physics of Fluids, Volume 32, Issue 11, November 2020.

Adaptive lattice Boltzmann methods (LBMs) are based on velocity discretizations that self-adjust to local macroscopic conditions such as velocity and temperature. While this feature improves the accuracy and the stability of LBMs for large velocity and temperature variations, it also strongly impacts the efficiency of the algorithm due to space interpolations that are required to get populations at grid nodes. To avoid this defect, the present work proposes new formulations of adaptive LBMs that do not rely anymore on space interpolations, hence drastically improving their parallel efficiency for the simulation of high-speed compressible flows. To reach this goal, the adaptive phase discretization is restricted to particular states that are compliant with the efficient “collide-and-stream” algorithm, and as a consequence, it does not require additional interpolation steps. The development of proper state-adaptive solvers with on-grid propagation imposes new restrictions and challenges on the discrete stencils, namely, the need for an extended operability range allowing for the transition between two phase discretizations. Achieving the minimum operability range for discrete polynomial equilibria requires rather large stencils (e.g., D2Q81, D2Q121) and is therefore not competitive for compressible flow simulations. However, as shown in this article, the use of numerical equilibria can provide for overlaps in the operability ranges of neighboring discrete shifts at acceptable cost using the D2Q21 lattice. Through several numerical validations, the present approach is shown to allow for an efficient realization of discrete state-adaptive LBMs for high Mach number flows even in the low-viscosity regime.

Adaptive lattice Boltzmann methods (LBMs) are based on velocity discretizations that self-adjust to local macroscopic conditions such as velocity and temperature. While this feature improves the accuracy and the stability of LBMs for large velocity and temperature variations, it also strongly impacts the efficiency of the algorithm due to space interpolations that are required to get populations at grid nodes. To avoid this defect, the present work proposes new formulations of adaptive LBMs that do not rely anymore on space interpolations, hence drastically improving their parallel efficiency for the simulation of high-speed compressible flows. To reach this goal, the adaptive phase discretization is restricted to particular states that are compliant with the efficient “collide-and-stream” algorithm, and as a consequence, it does not require additional interpolation steps. The development of proper state-adaptive solvers with on-grid propagation imposes new restrictions and challenges on the discrete stencils, namely, the need for an extended operability range allowing for the transition between two phase discretizations. Achieving the minimum operability range for discrete polynomial equilibria requires rather large stencils (e.g., D2Q81, D2Q121) and is therefore not competitive for compressible flow simulations. However, as shown in this article, the use of numerical equilibria can provide for overlaps in the operability ranges of neighboring discrete shifts at acceptable cost using the D2Q21 lattice. Through several numerical validations, the present approach is shown to allow for an efficient realization of discrete state-adaptive LBMs for high Mach number flows even in the low-viscosity regime.

Categories: Latest papers in fluid mechanics

### Study of spontaneous mobility and imbibition of a liquid droplet in contact with fibrous porous media considering wettability effects

Physics of Fluids, Volume 32, Issue 11, November 2020.

In this paper, droplet mobility and penetration into a fibrous porous medium are studied considering different physical and geometrical properties for the fibers. An in-depth insight into the droplet imbibition into the fibrous medium is beneficial for improving membrane products in different applications. Herein, a multiphase lattice Boltzmann method is employed as an efficient numerical algorithm for predicting the multiphase flow characteristics and the interfacial dynamics affected by the interaction between the droplet and fibrous substrates considered. This computational technique is validated by comparison of the present results obtained for different benchmark two-phase flow problems with those reported in the literature, which shows good agreement and confirms its accuracy and efficiency. Droplet spreading and penetration into the fibrous porous geometries are then studied considering various porous topologies, intrinsic contact angles, and fiber sizes. This study shows that the intrinsic contact angle has a great influence on the capillary pressure and, consequently, on the droplet imbibition into the porous medium. The droplet easily penetrates the porous substrate by decreasing the intrinsic contact angle of the fibers, and vice versa. It is also concluded that by coating the fibrous porous medium with a narrow layer of thin fibers, the surface resistance to liquid penetration significantly increases. The present results illustrate that the droplet size impacts the directional wicking ability of the fibrous porous structure used in this study. This property should be considered to produce appropriate two-layer membranes for different applications.

In this paper, droplet mobility and penetration into a fibrous porous medium are studied considering different physical and geometrical properties for the fibers. An in-depth insight into the droplet imbibition into the fibrous medium is beneficial for improving membrane products in different applications. Herein, a multiphase lattice Boltzmann method is employed as an efficient numerical algorithm for predicting the multiphase flow characteristics and the interfacial dynamics affected by the interaction between the droplet and fibrous substrates considered. This computational technique is validated by comparison of the present results obtained for different benchmark two-phase flow problems with those reported in the literature, which shows good agreement and confirms its accuracy and efficiency. Droplet spreading and penetration into the fibrous porous geometries are then studied considering various porous topologies, intrinsic contact angles, and fiber sizes. This study shows that the intrinsic contact angle has a great influence on the capillary pressure and, consequently, on the droplet imbibition into the porous medium. The droplet easily penetrates the porous substrate by decreasing the intrinsic contact angle of the fibers, and vice versa. It is also concluded that by coating the fibrous porous medium with a narrow layer of thin fibers, the surface resistance to liquid penetration significantly increases. The present results illustrate that the droplet size impacts the directional wicking ability of the fibrous porous structure used in this study. This property should be considered to produce appropriate two-layer membranes for different applications.

Categories: Latest papers in fluid mechanics

### Effect of radiation on thermosolutal Marangoni convection in a porous medium with chemical reaction and heat source/sink

Physics of Fluids, Volume 32, Issue 11, November 2020.

Thermosolutal Marangoni boundary layer flows are of great interest due to their applications in industrial applications such as drying of silicon wafers, thin layers of paint, glues, in heat exchangers, and crystal growth in space. The present analysis deals with the effect of chemical radiation and heat absorption/generation of the viscous fluid flow on a thermosolutal Marangoni porous boundary with mass transpiration and heat source/sink. The physical flow problem is mathematically modeled into Navier–Stokes equations. These nonlinear partial differential equations are then mapped into a set of nonlinear ordinary differential equations using similarity transformation. The analytical solutions for velocity, temperature, and concentration profiles are rigorously derived. The solutions so obtained are analyzed through various plots to demonstrate the effect of various physical parameters such as mass transpiration parameter Vc, inverse Darcy number Da−1, Marangoni number Ma, Schmidt number Sc, chemical reaction coefficient (K), Prandtl number (Pr), thermal radiation parameter (NR), and the heat source/sink parameter (I) on the momentum/thermal boundary, and their physical insights are also reported.

Thermosolutal Marangoni boundary layer flows are of great interest due to their applications in industrial applications such as drying of silicon wafers, thin layers of paint, glues, in heat exchangers, and crystal growth in space. The present analysis deals with the effect of chemical radiation and heat absorption/generation of the viscous fluid flow on a thermosolutal Marangoni porous boundary with mass transpiration and heat source/sink. The physical flow problem is mathematically modeled into Navier–Stokes equations. These nonlinear partial differential equations are then mapped into a set of nonlinear ordinary differential equations using similarity transformation. The analytical solutions for velocity, temperature, and concentration profiles are rigorously derived. The solutions so obtained are analyzed through various plots to demonstrate the effect of various physical parameters such as mass transpiration parameter Vc, inverse Darcy number Da−1, Marangoni number Ma, Schmidt number Sc, chemical reaction coefficient (K), Prandtl number (Pr), thermal radiation parameter (NR), and the heat source/sink parameter (I) on the momentum/thermal boundary, and their physical insights are also reported.

Categories: Latest papers in fluid mechanics

### Supersonic and near-equilibrium gas-driven granular flow

Physics of Fluids, Volume 32, Issue 11, November 2020.

Studies have found the surprising ability of hydrodynamic theory, which is based on the validity of the local thermodynamic equilibrium postulate, to capture the main features of shock waves in supersonic granular gases. However, its underlying mechanism remains unclear. To explore the factors underpinning the relationship between hydrodynamic theory and the behavior of shock waves in granular gases, a discrete particle method was used to systematically study gas-driven granular flow in gas–solid fluidized beds. It was shown that the flow of granular gases is typically supersonic, consistent with the previous understanding of shear granular flow. However, the Knudsen numbers and entropy criterion, which are used to quantify the distance from the local thermodynamic equilibrium state, were generally small. This finding explains why hydrodynamic theory can describe the behavior of supersonic granular flows; that is, shock waves in granular gases are locally near-equilibrium even though they are supersonic. This study also indicates that shock waves in ordinary gases and granular gases are fundamentally different.

Studies have found the surprising ability of hydrodynamic theory, which is based on the validity of the local thermodynamic equilibrium postulate, to capture the main features of shock waves in supersonic granular gases. However, its underlying mechanism remains unclear. To explore the factors underpinning the relationship between hydrodynamic theory and the behavior of shock waves in granular gases, a discrete particle method was used to systematically study gas-driven granular flow in gas–solid fluidized beds. It was shown that the flow of granular gases is typically supersonic, consistent with the previous understanding of shear granular flow. However, the Knudsen numbers and entropy criterion, which are used to quantify the distance from the local thermodynamic equilibrium state, were generally small. This finding explains why hydrodynamic theory can describe the behavior of supersonic granular flows; that is, shock waves in granular gases are locally near-equilibrium even though they are supersonic. This study also indicates that shock waves in ordinary gases and granular gases are fundamentally different.

Categories: Latest papers in fluid mechanics

### Effect of gradient wettability on capillary imbibition in open semicircular copper channel

Physics of Fluids, Volume 32, Issue 11, November 2020.

Open semicircular copper channels with a gradient wettability of 45°–3° or 3°–45° (contact angle of 1,2-propanediol), homogeneous wettability of 3°, and segmented wettability on their inner surfaces were constructed. The capillary imbibition of 1,2-propanediol in these channels demonstrates that, compared with the surface with homogeneous wettability, there are an additional driving force and resistance on the surfaces with a gradient wettability of 45°–3° and 3°–45°, respectively. Meanwhile, the channel with gradient wettability on the first half segment and homogeneous wettability on the second half segment could accelerate capillary imbibition better than that with gradient wettability on the whole channel. Furthermore, a smaller length ratio, i.e., length of gradient segment to that of homogeneous segment of the channel, demonstrates a better liquid acceleration effect. Based on the Lucas–Washburn equation, a theoretical model to describe capillary imbibition was established by introducing an additional force arisen from the positive gradient wettability and a retardation coefficient caused by the surface roughness. The flow front position vs flow time could be predicted by the established model in this work, and the relative error between the theoretical prediction and experimental result was less than 20.7%, indicating the rationality of the proposed model.

Open semicircular copper channels with a gradient wettability of 45°–3° or 3°–45° (contact angle of 1,2-propanediol), homogeneous wettability of 3°, and segmented wettability on their inner surfaces were constructed. The capillary imbibition of 1,2-propanediol in these channels demonstrates that, compared with the surface with homogeneous wettability, there are an additional driving force and resistance on the surfaces with a gradient wettability of 45°–3° and 3°–45°, respectively. Meanwhile, the channel with gradient wettability on the first half segment and homogeneous wettability on the second half segment could accelerate capillary imbibition better than that with gradient wettability on the whole channel. Furthermore, a smaller length ratio, i.e., length of gradient segment to that of homogeneous segment of the channel, demonstrates a better liquid acceleration effect. Based on the Lucas–Washburn equation, a theoretical model to describe capillary imbibition was established by introducing an additional force arisen from the positive gradient wettability and a retardation coefficient caused by the surface roughness. The flow front position vs flow time could be predicted by the established model in this work, and the relative error between the theoretical prediction and experimental result was less than 20.7%, indicating the rationality of the proposed model.

Categories: Latest papers in fluid mechanics