# Latest papers in fluid mechanics

### Improved fifth-order weighted essentially non-oscillatory scheme with low dissipation and high resolution for compressible flows

Physics of Fluids, Volume 34, Issue 5, May 2022.

Compressible flows are numerically simulated using hyperbolic conservation laws. This study proposes a modified fifth-order weighted essentially non-oscillatory (WENO) scheme with a relatively low dissipation and high resolution for hyperbolic conservation laws. This scheme exhibits good performance when solving complex compressible flow fields containing strong discontinuities and smooth microstructures. A simple local smoothness indicator and an eighth-order global smoothness indicator are introduced to improve the accuracy. Furthermore, we construct a new optimal coefficient, which can be adaptively adjusted with different states of the flow field. It no longer depends on the grid spacing. This adaptive coefficient not only reduces dissipation while improving the resolution but also prevents negative dissipation and effectively suppresses spurious numerical oscillations. The proposed scheme attains a higher accuracy at high-order critical points than three classical WENO schemes. Moreover, analysis of the approximate dispersion relation indicates that the proposed scheme provides good dispersion and dissipation properties compared with other WENO schemes. Finally, several standard numerical experiments are performed to demonstrate the enhanced performance of the proposed scheme. The numerical results indicate that the present scheme has a low dissipation, high resolution, and good stability to capture both smooth and discontinuous structures.

Compressible flows are numerically simulated using hyperbolic conservation laws. This study proposes a modified fifth-order weighted essentially non-oscillatory (WENO) scheme with a relatively low dissipation and high resolution for hyperbolic conservation laws. This scheme exhibits good performance when solving complex compressible flow fields containing strong discontinuities and smooth microstructures. A simple local smoothness indicator and an eighth-order global smoothness indicator are introduced to improve the accuracy. Furthermore, we construct a new optimal coefficient, which can be adaptively adjusted with different states of the flow field. It no longer depends on the grid spacing. This adaptive coefficient not only reduces dissipation while improving the resolution but also prevents negative dissipation and effectively suppresses spurious numerical oscillations. The proposed scheme attains a higher accuracy at high-order critical points than three classical WENO schemes. Moreover, analysis of the approximate dispersion relation indicates that the proposed scheme provides good dispersion and dissipation properties compared with other WENO schemes. Finally, several standard numerical experiments are performed to demonstrate the enhanced performance of the proposed scheme. The numerical results indicate that the present scheme has a low dissipation, high resolution, and good stability to capture both smooth and discontinuous structures.

Categories: Latest papers in fluid mechanics

### Collision of an acceleration wave with blast wave in van der Waals dusty reacting gases

Physics of Fluids, Volume 34, Issue 5, May 2022.

A system of hyperbolic partial differential equations describing a one-dimensional planar and radially symmetric flow of real dusty reacting gases is considered. The transport equation for an acceleration wave is obtained to analyze the evolution of the acceleration wave via a particular solution for the system under consideration. The Rankine–Hugoniot jump conditions across the blast wave are used to determine Lax entropy conditions for a physical blast wave. Furthermore, amplitudes of reflected waves, transmitted waves, and the bounce in shock acceleration, which arises from the collision between an acceleration wave and a blast wave, are determined.

A system of hyperbolic partial differential equations describing a one-dimensional planar and radially symmetric flow of real dusty reacting gases is considered. The transport equation for an acceleration wave is obtained to analyze the evolution of the acceleration wave via a particular solution for the system under consideration. The Rankine–Hugoniot jump conditions across the blast wave are used to determine Lax entropy conditions for a physical blast wave. Furthermore, amplitudes of reflected waves, transmitted waves, and the bounce in shock acceleration, which arises from the collision between an acceleration wave and a blast wave, are determined.

Categories: Latest papers in fluid mechanics

### Flow of gluten with tunable protein composition: From stress undershoot to stress overshoot and strain hardening

Physics of Fluids, Volume 34, Issue 5, May 2022.

Understanding the origin of the unique rheological properties of wheat gluten, the protein fraction of wheat grain, is crucial in bread-making processes and has raised questions of scientists for decades. Gluten is a complex mixture of two families of proteins, monomeric gliadins and polymeric glutenins. To better understand the respective role of the different classes of proteins in the supramolecular structure of gluten and its link to the material properties, we investigate here concentrated dispersions of gluten proteins in water with a fixed total protein concentration but variable composition in gliadin and glutenin. Linear viscoelasticity measurements show a gradual increase in the viscosity of the samples as the glutenin mass content increases from 7 to 66%. While the gliadin-rich samples are microphase-separated viscous fluids, homogeneous and transparent pre-gel and gels are obtained with the replacement of gliadin by glutenin. To unravel the flow properties of the gluten samples, we perform shear startup experiments at different shear-rates. In accordance with the linear viscoelastic signature, three classes of behavior are evidenced depending on the protein composition. As samples get depleted in gliadin and enriched in glutenin, distinctive features are measured: (i) viscosity undershoot suggesting droplet elongation for microphase-separated dispersions, (ii) stress overshoot and partial structural relaxation for near-critical pre-gels, and (iii) strain hardening and flow instabilities of gels. We discuss the experimental results by analogy with the behavior of model systems, including viscoelastic emulsions, branched polymer melts, and critical gels, and provide a consistent physical picture of the supramolecular features of the three classes of protein dispersions.

Understanding the origin of the unique rheological properties of wheat gluten, the protein fraction of wheat grain, is crucial in bread-making processes and has raised questions of scientists for decades. Gluten is a complex mixture of two families of proteins, monomeric gliadins and polymeric glutenins. To better understand the respective role of the different classes of proteins in the supramolecular structure of gluten and its link to the material properties, we investigate here concentrated dispersions of gluten proteins in water with a fixed total protein concentration but variable composition in gliadin and glutenin. Linear viscoelasticity measurements show a gradual increase in the viscosity of the samples as the glutenin mass content increases from 7 to 66%. While the gliadin-rich samples are microphase-separated viscous fluids, homogeneous and transparent pre-gel and gels are obtained with the replacement of gliadin by glutenin. To unravel the flow properties of the gluten samples, we perform shear startup experiments at different shear-rates. In accordance with the linear viscoelastic signature, three classes of behavior are evidenced depending on the protein composition. As samples get depleted in gliadin and enriched in glutenin, distinctive features are measured: (i) viscosity undershoot suggesting droplet elongation for microphase-separated dispersions, (ii) stress overshoot and partial structural relaxation for near-critical pre-gels, and (iii) strain hardening and flow instabilities of gels. We discuss the experimental results by analogy with the behavior of model systems, including viscoelastic emulsions, branched polymer melts, and critical gels, and provide a consistent physical picture of the supramolecular features of the three classes of protein dispersions.

Categories: Latest papers in fluid mechanics

### Numerical analysis of effect of Reynolds number on interaction of density-stratified fluid with a vortex ring

Physics of Fluids, Volume 34, Issue 5, May 2022.

In this study, the effect of Reynolds number (Re) on the mixing process of a two-layer density-stratified fluid, caused by the interaction between a vortex ring and the density interface, was numerically investigated using an improved vortex-in-cell method. The density-stratified fluid consisted of water (upper layer) and an aqueous sodium chloride solution (lower layer). Re of the simulated vortex ring was varied from 644 to 1932. We numerically investigated the behavior of the vortex ring and density-stratified fluid, and compared the same with that from a previously conducted experimental study from the literature. The vortex structure generated during the interaction was visualized in three dimensions. Furthermore, the mixing process was evaluated in terms of the stirring index, gradient of concentration, and stirring efficiency. The mixing behavior of the vortex ring was a function of the interaction pattern. For example, for a large Re, with the penetrative pattern, the stirring efficiency reached a constant value that was smaller than that from the partially penetrative pattern. The results showed that a strong stirring caused by an increase in Re of the vortex ring would not always lead to effective mixing.

In this study, the effect of Reynolds number (Re) on the mixing process of a two-layer density-stratified fluid, caused by the interaction between a vortex ring and the density interface, was numerically investigated using an improved vortex-in-cell method. The density-stratified fluid consisted of water (upper layer) and an aqueous sodium chloride solution (lower layer). Re of the simulated vortex ring was varied from 644 to 1932. We numerically investigated the behavior of the vortex ring and density-stratified fluid, and compared the same with that from a previously conducted experimental study from the literature. The vortex structure generated during the interaction was visualized in three dimensions. Furthermore, the mixing process was evaluated in terms of the stirring index, gradient of concentration, and stirring efficiency. The mixing behavior of the vortex ring was a function of the interaction pattern. For example, for a large Re, with the penetrative pattern, the stirring efficiency reached a constant value that was smaller than that from the partially penetrative pattern. The results showed that a strong stirring caused by an increase in Re of the vortex ring would not always lead to effective mixing.

Categories: Latest papers in fluid mechanics

### Supersonic cavity shear layer control using spanwise pulsed spark discharge array

Physics of Fluids, Volume 34, Issue 5, May 2022.

An experimental study on supersonic cavity flow control using a spanwise pulsed spark discharge array (SP-PSDA) is performed in this paper. High-speed schlieren imaging at a frame rate of 50 kHz is deployed for flow visualization. The schlieren snapshots, as well as their statistics, are analyzed to reveal the supersonic cavity flow control effect and its underlying mechanism. Results show that the shear layer presents a wave-like oscillation due to thermal bulbs induced by SP-PSDA. Specifically, the shear layer structure in the baseline case resembles an incomplete hairpin structure, which becomes complete after plasma actuation. SP-PSDA actuation at 5 kHz has a better control effect, which enhances the IRMS of the whole hairpin structure and produces several channels within it—these aid momentum transport within the shear layer. According to the results of proper orthogonal decomposition, the thermal bulbs couple with the shear layer to form large-scale coherent structures. These structures excite the Kelvin–Helmholtz instability, converting the oscillation frequency of the shear layer to an actuation frequency.

An experimental study on supersonic cavity flow control using a spanwise pulsed spark discharge array (SP-PSDA) is performed in this paper. High-speed schlieren imaging at a frame rate of 50 kHz is deployed for flow visualization. The schlieren snapshots, as well as their statistics, are analyzed to reveal the supersonic cavity flow control effect and its underlying mechanism. Results show that the shear layer presents a wave-like oscillation due to thermal bulbs induced by SP-PSDA. Specifically, the shear layer structure in the baseline case resembles an incomplete hairpin structure, which becomes complete after plasma actuation. SP-PSDA actuation at 5 kHz has a better control effect, which enhances the IRMS of the whole hairpin structure and produces several channels within it—these aid momentum transport within the shear layer. According to the results of proper orthogonal decomposition, the thermal bulbs couple with the shear layer to form large-scale coherent structures. These structures excite the Kelvin–Helmholtz instability, converting the oscillation frequency of the shear layer to an actuation frequency.

Categories: Latest papers in fluid mechanics

### Liquid dripping dynamics and levitation stability control of molten Ti–Al–Nb alloy within electromagnetic fields

Physics of Fluids, Volume 34, Issue 5, May 2022.

The dripping dynamics of the electromagnetically levitated (EML) liquid Ti–Al–Nb alloy under high temperatures was investigated by both numerical simulation based on the Arbitrary Lagrangian–Eulerian method and corresponding EML experiments. A dripping formation parameter εD was defined to describe the critical shape of alloy droplet. According to the simulated results, the high-temperature dripping phenomenon took place when εD < 0.68, which was in good agreement with experimental data. When dripping event occurred, the Lorentz force applied on alloy droplet decreased by approximately 11.7% within 0.07 s. Three typical methods were accordingly proposed to avoid the dripping failure of a bulk liquid Ti–Al–Nb alloy, which was implemented by enhancing electric current, adjusting levitation coil diameter, or increasing coil winding number. To control the droplet shape, the deformation pattern and the flow behavior of the liquid alloy were studied in a wide current range from 700 to 1400 A. With the increase in excitation current, the cone-shaped alloy melt transformed to a rhombus, and the flow behavior transformed from a typical four toroidal flow vortexes up to a complex eight toroidal flow vortexes. Moreover, the centroid position of liquid alloy rose up significantly at first and then slowly approached to levitation ceiling.

The dripping dynamics of the electromagnetically levitated (EML) liquid Ti–Al–Nb alloy under high temperatures was investigated by both numerical simulation based on the Arbitrary Lagrangian–Eulerian method and corresponding EML experiments. A dripping formation parameter εD was defined to describe the critical shape of alloy droplet. According to the simulated results, the high-temperature dripping phenomenon took place when εD < 0.68, which was in good agreement with experimental data. When dripping event occurred, the Lorentz force applied on alloy droplet decreased by approximately 11.7% within 0.07 s. Three typical methods were accordingly proposed to avoid the dripping failure of a bulk liquid Ti–Al–Nb alloy, which was implemented by enhancing electric current, adjusting levitation coil diameter, or increasing coil winding number. To control the droplet shape, the deformation pattern and the flow behavior of the liquid alloy were studied in a wide current range from 700 to 1400 A. With the increase in excitation current, the cone-shaped alloy melt transformed to a rhombus, and the flow behavior transformed from a typical four toroidal flow vortexes up to a complex eight toroidal flow vortexes. Moreover, the centroid position of liquid alloy rose up significantly at first and then slowly approached to levitation ceiling.

Categories: Latest papers in fluid mechanics

### Large eddy simulation of a thermal impinging jet using the lattice Boltzmann method

Physics of Fluids, Volume 34, Issue 5, May 2022.

A compressible Hybrid Lattice Boltzmann Method solver is used to perform a wall-resolved Large eddy simulation of an isothermal axisymmetric jet issuing from a pipe and impinging on a heated flat plate at a Reynolds number of 23 000, a Mach number of 0.1, and an impingement distance of two jet diameters. The jet flow field statistics, Nusselt number profile (including the secondary peak), and shear stress profile were well reproduced. The azimuthal coherence of the primary vortical structures was relatively low, leading to no discernible temporal periodicity of the azimuthally averaged Nusselt number at the location of the secondary peak. While local unsteady near-wall flow separation was observed in the wall jet, this flow separation did not exhibit azimuthal coherence and was not found to be the only cause of the thermal spots blue, which lead to the secondary peak in the Nusselt number, as stream-wise oriented structures also played a significant role in increasing the local heat transfer.

A compressible Hybrid Lattice Boltzmann Method solver is used to perform a wall-resolved Large eddy simulation of an isothermal axisymmetric jet issuing from a pipe and impinging on a heated flat plate at a Reynolds number of 23 000, a Mach number of 0.1, and an impingement distance of two jet diameters. The jet flow field statistics, Nusselt number profile (including the secondary peak), and shear stress profile were well reproduced. The azimuthal coherence of the primary vortical structures was relatively low, leading to no discernible temporal periodicity of the azimuthally averaged Nusselt number at the location of the secondary peak. While local unsteady near-wall flow separation was observed in the wall jet, this flow separation did not exhibit azimuthal coherence and was not found to be the only cause of the thermal spots blue, which lead to the secondary peak in the Nusselt number, as stream-wise oriented structures also played a significant role in increasing the local heat transfer.

Categories: Latest papers in fluid mechanics

### A method for partitioning the sources of aerodynamic loading noise in vortex dominated flows

Physics of Fluids, Volume 34, Issue 5, May 2022.

Aerodynamic loading noise is the primary noise component in a wide range of applications. While it is well known that the loading noise is generated by the time-varying aerodynamic forces on the surface, further segregation of the loading noise into the components related to the flow structures and fluid dynamic mechanisms would be useful in pinpointing the source mechanisms for this noise. In the present study, an aeroacoustic partitioning method which can decompose the loading noise into the components associated with their generation mechanism as well as specific vortex structures is proposed. The method combines a previously developed force partitioning method with acoustic analogy-based sound prediction. The method is applied to the canonical dipole sound generation by a circular cylinder as well as the loading noise generation by a pitching airfoil. The results demonstrate the ability of the method to identify the dominant loading noise generation mechanisms and enable quantification of the effect of the vortex structures around the body on the generation of the loading noise.

Aerodynamic loading noise is the primary noise component in a wide range of applications. While it is well known that the loading noise is generated by the time-varying aerodynamic forces on the surface, further segregation of the loading noise into the components related to the flow structures and fluid dynamic mechanisms would be useful in pinpointing the source mechanisms for this noise. In the present study, an aeroacoustic partitioning method which can decompose the loading noise into the components associated with their generation mechanism as well as specific vortex structures is proposed. The method combines a previously developed force partitioning method with acoustic analogy-based sound prediction. The method is applied to the canonical dipole sound generation by a circular cylinder as well as the loading noise generation by a pitching airfoil. The results demonstrate the ability of the method to identify the dominant loading noise generation mechanisms and enable quantification of the effect of the vortex structures around the body on the generation of the loading noise.

Categories: Latest papers in fluid mechanics

### Using gene expression programming to discover macroscopic governing equations hidden in the data of molecular simulations

Physics of Fluids, Volume 34, Issue 5, May 2022.

The unprecedented amount of data and the advancement of machine learning methods are driving the rapid development of data-driven modeling in the community of fluid mechanics. In this work, a data-driven strategy is developed by the combination of the direct simulation Monte Carlo (DSMC) method and the gene expression programming (GEP) method. DSMC is a molecular simulation method without any assumed macroscopic governing equations a priori and is employed to generate data of flow fields, while the enhanced GEP method is leveraged to discover governing equations. We first validate our idea using two benchmarks, such as the Burgers equation and Sine–Gordon equation. Then, we apply the strategy to discover governing equations hidden in the complex fluid dynamics. Our results demonstrate that in the continuum regime, the discovered equations are consistent with the traditional ones with linear constitutive relations, while in the non-continuum regime such as shock wave, the discovered equation comprises of high-order constitutive relations, which are similar to those in the Burnett equation but with modified coefficients. Compared to the Navier–Stokes–Fourier equations and the Burnett equation, the prediction of the viscous stress and heat flux in the shock wave via the presented data-driven model has the best match to the DSMC data. It is promising to extend the proposed data-driven strategy to more complex problems and discover hidden governing equations which may be unknown so far.

The unprecedented amount of data and the advancement of machine learning methods are driving the rapid development of data-driven modeling in the community of fluid mechanics. In this work, a data-driven strategy is developed by the combination of the direct simulation Monte Carlo (DSMC) method and the gene expression programming (GEP) method. DSMC is a molecular simulation method without any assumed macroscopic governing equations a priori and is employed to generate data of flow fields, while the enhanced GEP method is leveraged to discover governing equations. We first validate our idea using two benchmarks, such as the Burgers equation and Sine–Gordon equation. Then, we apply the strategy to discover governing equations hidden in the complex fluid dynamics. Our results demonstrate that in the continuum regime, the discovered equations are consistent with the traditional ones with linear constitutive relations, while in the non-continuum regime such as shock wave, the discovered equation comprises of high-order constitutive relations, which are similar to those in the Burnett equation but with modified coefficients. Compared to the Navier–Stokes–Fourier equations and the Burnett equation, the prediction of the viscous stress and heat flux in the shock wave via the presented data-driven model has the best match to the DSMC data. It is promising to extend the proposed data-driven strategy to more complex problems and discover hidden governing equations which may be unknown so far.

Categories: Latest papers in fluid mechanics

### Well-balanced discrete unified gas-kinetic scheme for two-phase systems

Physics of Fluids, Volume 34, Issue 5, May 2022.

In this paper, a well-balanced discrete unified gas-kinetic scheme (WB-DUGKS) is developed to capture the physical equilibrium state for two-phase fluid systems. Based on the strategies adopted in the well-balanced lattice Boltzmann equation (WB-LBE) [Z. Guo, “Well-balanced lattice Boltzmann model for two-phase systems,” Phys. Fluids 33, 031709 (2021)], a novel equilibrium distribution function and a modified force term are employed in the DUGKS framework. Unlike the LBE model, the time step in DUGKS is decoupled from the mesh size such that the numerical stability can be enhanced. First, the well-balanced properties of the method are validated by simulating a stationary droplet. The numerical results show that the WB-DUGKS can successfully reach an equilibrium state and exhibits superior numerical stability at low viscosity compared with the WB-LBE model. Then, the dynamic process of the coalescence of two droplets is simulated. The time scaling predicted by the present model is in good quantitatively agreement with the previous numerical results and experimental data. Overall, the proposed model provides a promising tool for simulating two-phase systems.

In this paper, a well-balanced discrete unified gas-kinetic scheme (WB-DUGKS) is developed to capture the physical equilibrium state for two-phase fluid systems. Based on the strategies adopted in the well-balanced lattice Boltzmann equation (WB-LBE) [Z. Guo, “Well-balanced lattice Boltzmann model for two-phase systems,” Phys. Fluids 33, 031709 (2021)], a novel equilibrium distribution function and a modified force term are employed in the DUGKS framework. Unlike the LBE model, the time step in DUGKS is decoupled from the mesh size such that the numerical stability can be enhanced. First, the well-balanced properties of the method are validated by simulating a stationary droplet. The numerical results show that the WB-DUGKS can successfully reach an equilibrium state and exhibits superior numerical stability at low viscosity compared with the WB-LBE model. Then, the dynamic process of the coalescence of two droplets is simulated. The time scaling predicted by the present model is in good quantitatively agreement with the previous numerical results and experimental data. Overall, the proposed model provides a promising tool for simulating two-phase systems.

Categories: Latest papers in fluid mechanics

### Physics of fluid flow in an hourglass (converging–diverging) microchannel

Physics of Fluids, Volume 34, Issue 5, May 2022.

This work presents the numerical and experimental study of flow physics and characterization in hourglass microchannels at different geometric and flow parameters such as convergence–divergence angle, width ratio, length, aspect ratio, and Reynolds number. The first part of the study discusses the importance of finding a unique length scale to represent an hourglass microchannel. This representative dimension is proposed at a distance of L/2.9 (L is the total length of the microchannel) from the inlet of the microchannel by using a frictional equivalence concept between uniform and hourglass microchannels. The proposed length scale is unique as it remains independent of geometric and flow variables. The study of local flow physics shows that this length scale identifies the region that governs the overall flow behavior of the microchannel. The results also show that the pressure drop is an inverse function of convergence–divergence angle and aspect ratio, whereas the width ratio and length are direct functions. In addition, the pressure drop shows linear behavior with the volume flow rate (Reynolds number) similar to that of a uniform microchannel except at a higher volume flow rate for convergence–divergence angle or higher width ratio. This non-linear behavior is explained with the help of hydrodynamic resistance and velocity streamlines in the last part of this study. Furthermore, the convergence–divergence angle and the width ratio are identified as critical parameters to characterize the flow. Overall, the present study gives insights into the influence of the convergence–divergence effect due to critical parameters on the flow characteristics, which could help design hourglass microchannels for many engineering applications.

This work presents the numerical and experimental study of flow physics and characterization in hourglass microchannels at different geometric and flow parameters such as convergence–divergence angle, width ratio, length, aspect ratio, and Reynolds number. The first part of the study discusses the importance of finding a unique length scale to represent an hourglass microchannel. This representative dimension is proposed at a distance of L/2.9 (L is the total length of the microchannel) from the inlet of the microchannel by using a frictional equivalence concept between uniform and hourglass microchannels. The proposed length scale is unique as it remains independent of geometric and flow variables. The study of local flow physics shows that this length scale identifies the region that governs the overall flow behavior of the microchannel. The results also show that the pressure drop is an inverse function of convergence–divergence angle and aspect ratio, whereas the width ratio and length are direct functions. In addition, the pressure drop shows linear behavior with the volume flow rate (Reynolds number) similar to that of a uniform microchannel except at a higher volume flow rate for convergence–divergence angle or higher width ratio. This non-linear behavior is explained with the help of hydrodynamic resistance and velocity streamlines in the last part of this study. Furthermore, the convergence–divergence angle and the width ratio are identified as critical parameters to characterize the flow. Overall, the present study gives insights into the influence of the convergence–divergence effect due to critical parameters on the flow characteristics, which could help design hourglass microchannels for many engineering applications.

Categories: Latest papers in fluid mechanics

### Statistically invariant eddy viscosity models

Physics of Fluids, Volume 34, Issue 5, May 2022.

We presently generalize existing two-equation Reynolds-averaged Navier–Stokes models by using recent advances in our understanding of the Lie symmetries of governing turbulence. The motivation for this and the necessary steps are laid out using the conventional terminology of turbulence modeling, without requiring deep knowledge about the mathematical concept of symmetries. For illustration purposes, these steps are applied to the standard k–ε model and the k–ω model. The so-modified k–ε model is applied to a wide range of canonical flows. For all of them, it is shown to match or even improve the performance of its classical counterpart and is, thus, shown to be more general than the original k–ε model.

We presently generalize existing two-equation Reynolds-averaged Navier–Stokes models by using recent advances in our understanding of the Lie symmetries of governing turbulence. The motivation for this and the necessary steps are laid out using the conventional terminology of turbulence modeling, without requiring deep knowledge about the mathematical concept of symmetries. For illustration purposes, these steps are applied to the standard k–ε model and the k–ω model. The so-modified k–ε model is applied to a wide range of canonical flows. For all of them, it is shown to match or even improve the performance of its classical counterpart and is, thus, shown to be more general than the original k–ε model.

Categories: Latest papers in fluid mechanics

### Effects of immiscible interface and particle channelization on particle dynamics of oblique oily sand jets

Physics of Fluids, Volume 34, Issue 5, May 2022.

This paper investigates the evolution of oblique sand jets passing through a thin layer of oil and entering stagnant water known as oily sand jets. The jet evolution parameters include the frontal position, the trajectory of particle clusters, the frontal width, the area of oily sand clusters, cloud velocities, and bursting times. Two scaling parameters, known as aspect ratio and particle to nozzle size ratio, were found to control the evolution of oily sand jets. The results show that the ratio of a nozzle to sand particle size can cause particle channelization, which can significantly alter the motion of particle clusters in stagnant water. Moreover, the aspect ratio indicating the correlation between sand mass and nozzle diameter describes the dispersion of particle clusters during the evolution of oily sand jets. The frontal width of the oily sand jet was measured during the experiment, and the results were compared with the width of vertical sand jets in water. The results show that the width of the oblique oily sand jets increased as oily sand jets descended into water. In addition, the frontal width of oily sand jets was found to be greater than the frontal width of vertical sand jets without an oil layer. Experimental observations indicated that the channelization effect is initiated when the nozzle diameter is more than 36 times of mean particle size. The centroid of oily sand jets in the vertical direction increased by 50% due to the channelization effect. A two-stage cluster bursting was observed due to the excess shear stress between the outer boundary of clusters and the ambient water. The bursting stages were called the primary and secondary bursting, and the onset of cluster bursting was extracted for both stages. It was found that the primary and secondary bursting times were longer in experiments without particle channelization. The mean shear stress acting on the oil layer was calculated based on the forces acting on the control volume. Particle channelization was found as the main factor affecting the magnitude of shear stress at the boundary of sand clusters.

This paper investigates the evolution of oblique sand jets passing through a thin layer of oil and entering stagnant water known as oily sand jets. The jet evolution parameters include the frontal position, the trajectory of particle clusters, the frontal width, the area of oily sand clusters, cloud velocities, and bursting times. Two scaling parameters, known as aspect ratio and particle to nozzle size ratio, were found to control the evolution of oily sand jets. The results show that the ratio of a nozzle to sand particle size can cause particle channelization, which can significantly alter the motion of particle clusters in stagnant water. Moreover, the aspect ratio indicating the correlation between sand mass and nozzle diameter describes the dispersion of particle clusters during the evolution of oily sand jets. The frontal width of the oily sand jet was measured during the experiment, and the results were compared with the width of vertical sand jets in water. The results show that the width of the oblique oily sand jets increased as oily sand jets descended into water. In addition, the frontal width of oily sand jets was found to be greater than the frontal width of vertical sand jets without an oil layer. Experimental observations indicated that the channelization effect is initiated when the nozzle diameter is more than 36 times of mean particle size. The centroid of oily sand jets in the vertical direction increased by 50% due to the channelization effect. A two-stage cluster bursting was observed due to the excess shear stress between the outer boundary of clusters and the ambient water. The bursting stages were called the primary and secondary bursting, and the onset of cluster bursting was extracted for both stages. It was found that the primary and secondary bursting times were longer in experiments without particle channelization. The mean shear stress acting on the oil layer was calculated based on the forces acting on the control volume. Particle channelization was found as the main factor affecting the magnitude of shear stress at the boundary of sand clusters.

Categories: Latest papers in fluid mechanics

### Energy preserving reduced-order modeling of the rotating thermal shallow water equation

Physics of Fluids, Volume 34, Issue 5, May 2022.

In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The high fidelity full solutions are obtained by discretizing the RTSWE in space with skew-symmetric finite-differences, while preserving the Hamiltonian structure. The resulting skew-gradient system is integrated in time by the energy preserving average vector field (AVF) method. The ROM is constructed by applying proper orthogonal decomposition with the Galerkin projection, preserving the reduced skew-gradient structure, and integrating in time with the AVF method. The nonlinear terms of the Poisson matrix and Hamiltonian are approximated with the discrete empirical interpolation method to reduce the computational cost. The solutions of the resulting linear-quadratic reduced system are accelerated by the use of tensor techniques. The accuracy and computational efficiency of the ROMs are demonstrated for a numerical test problem. Preservation of the energy (Hamiltonian) and other conserved quantities, i.e., mass, buoyancy, and total vorticity, show that the reduced-order solutions ensure the long-term stability of the solutions while exhibiting several orders of magnitude computational speedup over the full-order model. Furthermore, we show that the ROMs are able to accurately predict the test and training data and capture the system behavior in the prediction phase.

In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The high fidelity full solutions are obtained by discretizing the RTSWE in space with skew-symmetric finite-differences, while preserving the Hamiltonian structure. The resulting skew-gradient system is integrated in time by the energy preserving average vector field (AVF) method. The ROM is constructed by applying proper orthogonal decomposition with the Galerkin projection, preserving the reduced skew-gradient structure, and integrating in time with the AVF method. The nonlinear terms of the Poisson matrix and Hamiltonian are approximated with the discrete empirical interpolation method to reduce the computational cost. The solutions of the resulting linear-quadratic reduced system are accelerated by the use of tensor techniques. The accuracy and computational efficiency of the ROMs are demonstrated for a numerical test problem. Preservation of the energy (Hamiltonian) and other conserved quantities, i.e., mass, buoyancy, and total vorticity, show that the reduced-order solutions ensure the long-term stability of the solutions while exhibiting several orders of magnitude computational speedup over the full-order model. Furthermore, we show that the ROMs are able to accurately predict the test and training data and capture the system behavior in the prediction phase.

Categories: Latest papers in fluid mechanics

### Measuring the effects of a pulsed excitation on the buildup of acoustic streaming and the acoustic radiation force utilizing an optical tweezer

Author(s): Christoph Goering and Jürg Dual

Pulsed excitations of piezoelectric transducers affect during the buildup the force contributions from acoustic streaming (AS) and the acoustic radiation force (ARF) to the total force in a standing pressure wave differently. We find with an optical tweezer as measuring instrument that during the fi…

[Phys. Rev. E 105, 055103] Published Fri May 13, 2022

Categories: Latest papers in fluid mechanics

### Effect of anode channel shape and wettability on CO2 bubble evolution in direct methanol fuel cells

Physics of Fluids, Volume 34, Issue 5, May 2022.

Active direct-methanol fuel cells operate on a liquid supply of reactants to the anode flow channels. Gaseous carbon dioxide is produced during operation forming large bubbles on the top side of diffusion layer, limiting the transport of reactants to the functional layer. This causes a significant drop in the rate of reaction and therefore limits the maximum current density. To collect CO2 bubbles away from the diffusion layer, a new design is proposed. It includes a degassing channel placed at the top of the main trapezoidal anode channel. The wettability of the degassing channel and the dihedral angle of the anode channel are investigated. To assess the effect of these parameters, a three-dimensional, two-phase flow model is developed and numerically simulated. Results show that adding the degassing channel is advantageous in terms of bubble collection. A trapezoidal main channel achieves a significantly higher rate of bubble actuation compared to a rectangular channel. In addition, using a dihedral angle of 20° causes a decrease in the pumping pressure, which reduces pumping losses. Moreover, a contact angle of 100° for the degassing channel provides the best compromise in terms of actuation rate, extraction rate out of the channel, and pressure drop along the channel. However, degassing channels can yield up to three times longer bubbles, which are around 75% slower. These findings create the opportunity to improve the performance of direct-methanol fuel cells by enhancing/optimizing the mass transport of reactants on the anode side.

Active direct-methanol fuel cells operate on a liquid supply of reactants to the anode flow channels. Gaseous carbon dioxide is produced during operation forming large bubbles on the top side of diffusion layer, limiting the transport of reactants to the functional layer. This causes a significant drop in the rate of reaction and therefore limits the maximum current density. To collect CO2 bubbles away from the diffusion layer, a new design is proposed. It includes a degassing channel placed at the top of the main trapezoidal anode channel. The wettability of the degassing channel and the dihedral angle of the anode channel are investigated. To assess the effect of these parameters, a three-dimensional, two-phase flow model is developed and numerically simulated. Results show that adding the degassing channel is advantageous in terms of bubble collection. A trapezoidal main channel achieves a significantly higher rate of bubble actuation compared to a rectangular channel. In addition, using a dihedral angle of 20° causes a decrease in the pumping pressure, which reduces pumping losses. Moreover, a contact angle of 100° for the degassing channel provides the best compromise in terms of actuation rate, extraction rate out of the channel, and pressure drop along the channel. However, degassing channels can yield up to three times longer bubbles, which are around 75% slower. These findings create the opportunity to improve the performance of direct-methanol fuel cells by enhancing/optimizing the mass transport of reactants on the anode side.

Categories: Latest papers in fluid mechanics

### Characterizing the non-Newtonian viscosity of high-solids drilling fluid dispersions by flow loop

Physics of Fluids, Volume 34, Issue 5, May 2022.

Increasing the speed of drilling operations is of commercial and military interest for transportation infrastructure as well as rapid installation of underground utilities in urban settings and over long distances. A significant challenge to increasing speed in horizontal directional drilling is pressure and flow rate management of drilling fluids circulating into and out of the borehole, removing solids cut free by the drill bit. The mixture of solids and drilling fluid results in a highly complex fluid dispersion, typically with a shear-thinning continuum. It is challenging to characterize the viscometric behavior of these dispersions, and such data are limited in the literature. It is increasingly important to understand and accurately model the viscosity of these dispersions since high drilling speeds increase the drilling fluid flow rate, approaching the pressure limits that borehole walls can withstand before failure. In this work, we characterize the viscometric properties of a drill test and model drilling fluid dispersion in a custom-built flow loop with solid concentrations up to 45 wt. %. The fluid viscosity is reported in terms of power-law parameters, which can be used to predict the pressure drop during real drilling conditions. We found a significant difference in the viscometric response between the drill test and model drilling fluid dispersions. The Shields parameter can capture the influence of solids settling on the measurable pressure losses. An important conclusion is that even model drilling fluid dispersions prepared with geotechnical data from a drill site may have significantly different viscometric characteristics than those relevant during a drilling operation.

Increasing the speed of drilling operations is of commercial and military interest for transportation infrastructure as well as rapid installation of underground utilities in urban settings and over long distances. A significant challenge to increasing speed in horizontal directional drilling is pressure and flow rate management of drilling fluids circulating into and out of the borehole, removing solids cut free by the drill bit. The mixture of solids and drilling fluid results in a highly complex fluid dispersion, typically with a shear-thinning continuum. It is challenging to characterize the viscometric behavior of these dispersions, and such data are limited in the literature. It is increasingly important to understand and accurately model the viscosity of these dispersions since high drilling speeds increase the drilling fluid flow rate, approaching the pressure limits that borehole walls can withstand before failure. In this work, we characterize the viscometric properties of a drill test and model drilling fluid dispersion in a custom-built flow loop with solid concentrations up to 45 wt. %. The fluid viscosity is reported in terms of power-law parameters, which can be used to predict the pressure drop during real drilling conditions. We found a significant difference in the viscometric response between the drill test and model drilling fluid dispersions. The Shields parameter can capture the influence of solids settling on the measurable pressure losses. An important conclusion is that even model drilling fluid dispersions prepared with geotechnical data from a drill site may have significantly different viscometric characteristics than those relevant during a drilling operation.

Categories: Latest papers in fluid mechanics

### Scattering of flexural-gravity waves due to a crack in a floating ice sheet in a two-layer fluid in the context of blocking dynamics

Physics of Fluids, Volume 34, Issue 5, May 2022.

The influence of wave blocking on the scattering of a flexural-gravity wave by a linear crack in a thin ice cover resting over a two-layer ocean having a rigid flat seafloor is investigated. The wave dispersion curve reveals the existence of multiple propagating wave modes within the blocking frequencies, either in the surface or interface mode. The Sommerfeld radiation condition depends on multiple propagating wave modes within the blocking frequency and contributes to wave energy propagation. The solution process involves the appropriate transition of wave modes within the blocking frequencies, which is obtained with the help of the dispersion curve. The reflection and transmission coefficients are generalized in the case of multiple propagating wave modes, and the associated energy balance relation is derived using Green's integral theorem. The scattering matrix is generated to describe all the possible transmitted and incident wave modes. The role of lateral compressive force and the density ratio on the scattering process, ice deflection, and interface elevation are shown graphically. This study reveals the occurrence of removable and jump discontinuities in the reflection and transmission coefficients at the saddle point as well as blocking frequencies and at the frequency for which incident wave mode changes. Irregular plate deflection and interface elevation patterns are found due to the superposition of multiple propagating wave modes within the primary and secondary blocking frequencies.

The influence of wave blocking on the scattering of a flexural-gravity wave by a linear crack in a thin ice cover resting over a two-layer ocean having a rigid flat seafloor is investigated. The wave dispersion curve reveals the existence of multiple propagating wave modes within the blocking frequencies, either in the surface or interface mode. The Sommerfeld radiation condition depends on multiple propagating wave modes within the blocking frequency and contributes to wave energy propagation. The solution process involves the appropriate transition of wave modes within the blocking frequencies, which is obtained with the help of the dispersion curve. The reflection and transmission coefficients are generalized in the case of multiple propagating wave modes, and the associated energy balance relation is derived using Green's integral theorem. The scattering matrix is generated to describe all the possible transmitted and incident wave modes. The role of lateral compressive force and the density ratio on the scattering process, ice deflection, and interface elevation are shown graphically. This study reveals the occurrence of removable and jump discontinuities in the reflection and transmission coefficients at the saddle point as well as blocking frequencies and at the frequency for which incident wave mode changes. Irregular plate deflection and interface elevation patterns are found due to the superposition of multiple propagating wave modes within the primary and secondary blocking frequencies.

Categories: Latest papers in fluid mechanics

### Wake characteristics of complex-shaped snow particles: Comparison of numerical simulations with fixed snowflakes to time-resolved particle tracking velocimetry experiments with free-falling analogs

Physics of Fluids, Volume 34, Issue 5, May 2022.

Experimental and numerical approaches have their own advantages and limitations, in particular, when dealing with complex phenomena such as snow particles falling at moderate Reynolds numbers (Re). Time-resolved, three-dimensional particle tracking velocimetry (4D-PTV) experiments of free-falling, three-dimensional (3D)-printed snowflakes' analogs shed light on the elaborate falling dynamics of irregular snow particles but present a lower resolution (tracer seeding density) and a limited field of view (domain size) to fully capture the wake flow. Delayed-detached eddy simulations of fixed snow particles do not realistically represent all the physics of a falling ice particle, especially for cases with unsteady falling attitudes, but accurately predict the drag coefficient and capture the wake characteristics for steadily falling snowflakes. In this work, we compare both approaches on time- and space-averaged flow quantities in the snowflake wake. First, we cross validate the two approaches for low Re cases, where close agreement of the wake features is expected, and second, we assess how strongly the unsteady falling motion perturbs the average wake pattern as compared to a fixed particle at higher Re. For steadily falling snowflakes, the fixed-particle model can properly represent the wake flow with errors within the experimental uncertainty (±15%). At moderate/high Re (unsteady falling motion), larger differences are present. Applying a co-moving frame to the experimental data to account for the particle movement or filtering the numerical data on larger grids reduces these differences only to some extent, implying that an unsteady fall significantly alters the average wake structure as compared to a fixed particle model.

Experimental and numerical approaches have their own advantages and limitations, in particular, when dealing with complex phenomena such as snow particles falling at moderate Reynolds numbers (Re). Time-resolved, three-dimensional particle tracking velocimetry (4D-PTV) experiments of free-falling, three-dimensional (3D)-printed snowflakes' analogs shed light on the elaborate falling dynamics of irregular snow particles but present a lower resolution (tracer seeding density) and a limited field of view (domain size) to fully capture the wake flow. Delayed-detached eddy simulations of fixed snow particles do not realistically represent all the physics of a falling ice particle, especially for cases with unsteady falling attitudes, but accurately predict the drag coefficient and capture the wake characteristics for steadily falling snowflakes. In this work, we compare both approaches on time- and space-averaged flow quantities in the snowflake wake. First, we cross validate the two approaches for low Re cases, where close agreement of the wake features is expected, and second, we assess how strongly the unsteady falling motion perturbs the average wake pattern as compared to a fixed particle at higher Re. For steadily falling snowflakes, the fixed-particle model can properly represent the wake flow with errors within the experimental uncertainty (±15%). At moderate/high Re (unsteady falling motion), larger differences are present. Applying a co-moving frame to the experimental data to account for the particle movement or filtering the numerical data on larger grids reduces these differences only to some extent, implying that an unsteady fall significantly alters the average wake structure as compared to a fixed particle model.

Categories: Latest papers in fluid mechanics

### Influence of vibrating wall on microswimmer migration in a channel

Physics of Fluids, Volume 34, Issue 5, May 2022.

The migration of microorganisms or synthetic microscale robots is always affected by the local environment, such as the surrounding fluid or muscular contractions. This paper describes a numerical study and asymptotic analysis of the influence of a moving boundary on the migration of a microswimmer in a channel. The locomotion of a finite swimmer between vibrating walls is simulated with both a beating and motionless flagellum. The swimmer can be propelled by the wall vibration, and this propulsion is independent of the self-propulsion of the beating flagellum. To reveal the influence of the vibrating walls, asymptotic analysis is applied to two models, one with an infinitely long filament placed at the channel center and another with an infinitesimally small swimmer. The results show that the vibrating wall effect depends on the ratio of the distance between the walls to the wavelength. The wall effect functions for the two models are obtained for both two-dimensional and circular channels. The finite swimmer in the two-dimensional channel moves with the velocity of the flow induced by the vibrating wall, rather than the swimming speed of the infinite filament. However, in the circular channel, there is no difference between the migration speeds of the two models, and the range of the wall influence is much larger than in the two-dimensional case.

The migration of microorganisms or synthetic microscale robots is always affected by the local environment, such as the surrounding fluid or muscular contractions. This paper describes a numerical study and asymptotic analysis of the influence of a moving boundary on the migration of a microswimmer in a channel. The locomotion of a finite swimmer between vibrating walls is simulated with both a beating and motionless flagellum. The swimmer can be propelled by the wall vibration, and this propulsion is independent of the self-propulsion of the beating flagellum. To reveal the influence of the vibrating walls, asymptotic analysis is applied to two models, one with an infinitely long filament placed at the channel center and another with an infinitesimally small swimmer. The results show that the vibrating wall effect depends on the ratio of the distance between the walls to the wavelength. The wall effect functions for the two models are obtained for both two-dimensional and circular channels. The finite swimmer in the two-dimensional channel moves with the velocity of the flow induced by the vibrating wall, rather than the swimming speed of the infinite filament. However, in the circular channel, there is no difference between the migration speeds of the two models, and the range of the wall influence is much larger than in the two-dimensional case.

Categories: Latest papers in fluid mechanics