# Latest papers in fluid mechanics

### Experimental observation of flow-induced vibrations of a transversely oscillating D-section prism

Physics of Fluids, Volume 33, Issue 9, September 2021.

Fluid–structure interactions of non-circular prisms are of significance from a scientific and practical viewpoint. In this paper, we present a new experimental observation of flow-induced vibrations and associated spectral characteristics of a transversely oscillating D-section prism at an angle of attack α varying from 0° to 180°, where α = 0° and 180° represent the configuration with the upstream curved and flat part, respectively. The Reynolds number range is 530–9620, and the reduced velocity range is 1–32, based on the projected prism width in the crossflow direction. The mass ratio of the prism is 11.35, and the structural damping ratio in still water is 0.0036. Based on the response amplitudes and spectral traits, the D-prism exhibits the typical vortex-induced vibration (VIV) at α = 0°–30°, the first transition response at α = 45°–60°, the small-amplitude VIV response at α = 105°–135°, the second transition response at α = 150°–165°, the combined VIV-galloping response at α = 90°, and the pure galloping at α = 75° and 180°. The second transition response between low- and high-amplitude branches is found to be hysteretic and intermittent. Flow physics behind the D-prism responses are further elucidated by the wake patterns based on a high-speed camera and the flow velocity spectra downstream of the prism.

Fluid–structure interactions of non-circular prisms are of significance from a scientific and practical viewpoint. In this paper, we present a new experimental observation of flow-induced vibrations and associated spectral characteristics of a transversely oscillating D-section prism at an angle of attack α varying from 0° to 180°, where α = 0° and 180° represent the configuration with the upstream curved and flat part, respectively. The Reynolds number range is 530–9620, and the reduced velocity range is 1–32, based on the projected prism width in the crossflow direction. The mass ratio of the prism is 11.35, and the structural damping ratio in still water is 0.0036. Based on the response amplitudes and spectral traits, the D-prism exhibits the typical vortex-induced vibration (VIV) at α = 0°–30°, the first transition response at α = 45°–60°, the small-amplitude VIV response at α = 105°–135°, the second transition response at α = 150°–165°, the combined VIV-galloping response at α = 90°, and the pure galloping at α = 75° and 180°. The second transition response between low- and high-amplitude branches is found to be hysteretic and intermittent. Flow physics behind the D-prism responses are further elucidated by the wake patterns based on a high-speed camera and the flow velocity spectra downstream of the prism.

Categories: Latest papers in fluid mechanics

### Rapid droplet spreading on a hot substrate

Physics of Fluids, Volume 33, Issue 9, September 2021.

Due to its high efficiency, droplet spray cooling is widely used in various industrial and scientific applications. The spreading of droplets can greatly affect heat transfer, and temperature can also affect the dynamics of droplet spreading. In this study, both experiment and numerical simulations are used to investigate the effects of temperature on droplet spreading on a hot substrate from the nanoscale dynamics of moving contact lines to macroscale thermo-capillary flows. It is found that with increasing substrate temperature, during fast droplet spreading, satellite droplets transit from first-stage pinch-off to second-stage pinch-off and then to no pinch-off. These phenomena can be attributed to the effects of temperature at different scales. In the nanoscale region of moving contact lines, temperature and corresponding viscosity can alter the dynamic wetting angle of the moving contact lines. At the microscale interface region, temperature can change the viscosity near droplet interfaces, leading to variation in the viscous force. At the macroscale droplet region, the temperature of a droplet can change its surface tension, leading to thermo-capillary flow along the droplet interface. The pinch-off dynamics of droplet spreading on hot substrate can be analyzed according to the propagation of interfacial capillary waves at different temperatures and the resultant neck dynamics. These findings provide insight into droplet-spreading regimes on hot substrates under different temperatures.

Due to its high efficiency, droplet spray cooling is widely used in various industrial and scientific applications. The spreading of droplets can greatly affect heat transfer, and temperature can also affect the dynamics of droplet spreading. In this study, both experiment and numerical simulations are used to investigate the effects of temperature on droplet spreading on a hot substrate from the nanoscale dynamics of moving contact lines to macroscale thermo-capillary flows. It is found that with increasing substrate temperature, during fast droplet spreading, satellite droplets transit from first-stage pinch-off to second-stage pinch-off and then to no pinch-off. These phenomena can be attributed to the effects of temperature at different scales. In the nanoscale region of moving contact lines, temperature and corresponding viscosity can alter the dynamic wetting angle of the moving contact lines. At the microscale interface region, temperature can change the viscosity near droplet interfaces, leading to variation in the viscous force. At the macroscale droplet region, the temperature of a droplet can change its surface tension, leading to thermo-capillary flow along the droplet interface. The pinch-off dynamics of droplet spreading on hot substrate can be analyzed according to the propagation of interfacial capillary waves at different temperatures and the resultant neck dynamics. These findings provide insight into droplet-spreading regimes on hot substrates under different temperatures.

Categories: Latest papers in fluid mechanics

### Rapid droplet spreading on a hot substrate

Physics of Fluids, Volume 33, Issue 9, September 2021.

Due to its high efficiency, droplet spray cooling is widely used in various industrial and scientific applications. The spreading of droplets can greatly affect heat transfer, and temperature can also affect the dynamics of droplet spreading. In this study, both experiment and numerical simulations are used to investigate the effects of temperature on droplet spreading on a hot substrate from the nanoscale dynamics of moving contact lines to macroscale thermo-capillary flows. It is found that with increasing substrate temperature, during fast droplet spreading, satellite droplets transit from first-stage pinch-off to second-stage pinch-off and then to no pinch-off. These phenomena can be attributed to the effects of temperature at different scales. In the nanoscale region of moving contact lines, temperature and corresponding viscosity can alter the dynamic wetting angle of the moving contact lines. At the microscale interface region, temperature can change the viscosity near droplet interfaces, leading to variation in the viscous force. At the macroscale droplet region, the temperature of a droplet can change its surface tension, leading to thermo-capillary flow along the droplet interface. The pinch-off dynamics of droplet spreading on hot substrate can be analyzed according to the propagation of interfacial capillary waves at different temperatures and the resultant neck dynamics. These findings provide insight into droplet-spreading regimes on hot substrates under different temperatures.

Due to its high efficiency, droplet spray cooling is widely used in various industrial and scientific applications. The spreading of droplets can greatly affect heat transfer, and temperature can also affect the dynamics of droplet spreading. In this study, both experiment and numerical simulations are used to investigate the effects of temperature on droplet spreading on a hot substrate from the nanoscale dynamics of moving contact lines to macroscale thermo-capillary flows. It is found that with increasing substrate temperature, during fast droplet spreading, satellite droplets transit from first-stage pinch-off to second-stage pinch-off and then to no pinch-off. These phenomena can be attributed to the effects of temperature at different scales. In the nanoscale region of moving contact lines, temperature and corresponding viscosity can alter the dynamic wetting angle of the moving contact lines. At the microscale interface region, temperature can change the viscosity near droplet interfaces, leading to variation in the viscous force. At the macroscale droplet region, the temperature of a droplet can change its surface tension, leading to thermo-capillary flow along the droplet interface. The pinch-off dynamics of droplet spreading on hot substrate can be analyzed according to the propagation of interfacial capillary waves at different temperatures and the resultant neck dynamics. These findings provide insight into droplet-spreading regimes on hot substrates under different temperatures.

Categories: Latest papers in fluid mechanics

### Special topic on turbulent and multiphase flows

Physics of Fluids, Volume 33, Issue 9, September 2021.

Categories: Latest papers in fluid mechanics

### Special topic on turbulent and multiphase flows

Physics of Fluids, Volume 33, Issue 9, September 2021.

Categories: Latest papers in fluid mechanics

### Synthetic near-wall small-scale turbulence and its application in wall-modeled large-eddy simulation

Physics of Fluids, Volume 33, Issue 9, September 2021.

A suitable representation of the universal near-wall small-scale motions helps the understanding of physical mechanisms as well as the development of simulation techniques of wall turbulence. Minimum flow unit (MFU) as a reduced-order model of wall turbulence serves the purpose, but requires non-trivial computational cost. Motivated by improving the MFU-based near-wall turbulence prediction model [Yin et al., “Prediction of near-wall turbulence using minimal flow unit,” J. Fluid Mech. 841, 654–673 (2018)] for better use in large-eddy simulations (LES), the present study seeks to supply near-wall small-scale turbulence fluctuations with synthetic flow fields generated from universal model of MFU, thus avoiding the auxiliary simulation and lowering the computational cost. We first obtain MFU data ranging from [math] to 8000 using direct numerical simulations and reconstruct 3-dimensional space–time spectra of MFU using the generalized local modulated wave method. The space–time spectra serve as the universal model of near-wall small-scale turbulence. We then propose a method to generate turbulent flow fields from space–time spectra, based on the synthetic random Fourier method. The generated flow is statistically consistent with and structurally similar to the authentic MFU. At last, the generated flow fields at different Reynolds numbers are applied to LES of off-wall channels, and the reasonable results obtained suggest that our synthetic near-wall small-scale turbulence is as effective as authentic MFU in constructing off-wall boundary conditions.

A suitable representation of the universal near-wall small-scale motions helps the understanding of physical mechanisms as well as the development of simulation techniques of wall turbulence. Minimum flow unit (MFU) as a reduced-order model of wall turbulence serves the purpose, but requires non-trivial computational cost. Motivated by improving the MFU-based near-wall turbulence prediction model [Yin et al., “Prediction of near-wall turbulence using minimal flow unit,” J. Fluid Mech. 841, 654–673 (2018)] for better use in large-eddy simulations (LES), the present study seeks to supply near-wall small-scale turbulence fluctuations with synthetic flow fields generated from universal model of MFU, thus avoiding the auxiliary simulation and lowering the computational cost. We first obtain MFU data ranging from [math] to 8000 using direct numerical simulations and reconstruct 3-dimensional space–time spectra of MFU using the generalized local modulated wave method. The space–time spectra serve as the universal model of near-wall small-scale turbulence. We then propose a method to generate turbulent flow fields from space–time spectra, based on the synthetic random Fourier method. The generated flow is statistically consistent with and structurally similar to the authentic MFU. At last, the generated flow fields at different Reynolds numbers are applied to LES of off-wall channels, and the reasonable results obtained suggest that our synthetic near-wall small-scale turbulence is as effective as authentic MFU in constructing off-wall boundary conditions.

Categories: Latest papers in fluid mechanics

### Synthetic near-wall small-scale turbulence and its application in wall-modeled large-eddy simulation

Physics of Fluids, Volume 33, Issue 9, September 2021.

A suitable representation of the universal near-wall small-scale motions helps the understanding of physical mechanisms as well as the development of simulation techniques of wall turbulence. Minimum flow unit (MFU) as a reduced-order model of wall turbulence serves the purpose, but requires non-trivial computational cost. Motivated by improving the MFU-based near-wall turbulence prediction model [Yin et al., “Prediction of near-wall turbulence using minimal flow unit,” J. Fluid Mech. 841, 654–673 (2018)] for better use in large-eddy simulations (LES), the present study seeks to supply near-wall small-scale turbulence fluctuations with synthetic flow fields generated from universal model of MFU, thus avoiding the auxiliary simulation and lowering the computational cost. We first obtain MFU data ranging from [math] to 8000 using direct numerical simulations and reconstruct 3-dimensional space–time spectra of MFU using the generalized local modulated wave method. The space–time spectra serve as the universal model of near-wall small-scale turbulence. We then propose a method to generate turbulent flow fields from space–time spectra, based on the synthetic random Fourier method. The generated flow is statistically consistent with and structurally similar to the authentic MFU. At last, the generated flow fields at different Reynolds numbers are applied to LES of off-wall channels, and the reasonable results obtained suggest that our synthetic near-wall small-scale turbulence is as effective as authentic MFU in constructing off-wall boundary conditions.

A suitable representation of the universal near-wall small-scale motions helps the understanding of physical mechanisms as well as the development of simulation techniques of wall turbulence. Minimum flow unit (MFU) as a reduced-order model of wall turbulence serves the purpose, but requires non-trivial computational cost. Motivated by improving the MFU-based near-wall turbulence prediction model [Yin et al., “Prediction of near-wall turbulence using minimal flow unit,” J. Fluid Mech. 841, 654–673 (2018)] for better use in large-eddy simulations (LES), the present study seeks to supply near-wall small-scale turbulence fluctuations with synthetic flow fields generated from universal model of MFU, thus avoiding the auxiliary simulation and lowering the computational cost. We first obtain MFU data ranging from [math] to 8000 using direct numerical simulations and reconstruct 3-dimensional space–time spectra of MFU using the generalized local modulated wave method. The space–time spectra serve as the universal model of near-wall small-scale turbulence. We then propose a method to generate turbulent flow fields from space–time spectra, based on the synthetic random Fourier method. The generated flow is statistically consistent with and structurally similar to the authentic MFU. At last, the generated flow fields at different Reynolds numbers are applied to LES of off-wall channels, and the reasonable results obtained suggest that our synthetic near-wall small-scale turbulence is as effective as authentic MFU in constructing off-wall boundary conditions.

Categories: Latest papers in fluid mechanics

### Instability of mixed convection flow in a differentially heated channel under a transverse magnetic field with internal heating

Physics of Fluids, Volume 33, Issue 9, September 2021.

This paper reports the linear stability of laminar magnetohydrodynamic (MHD) mixed convection flow in a differentially heated channel under a transverse magnetic field with the internal heating. Three different electrically conducting fluids, such as liquid mercury, water-based electrolytes, and Flibe (a molten salt mixture of lithium fluoride and beryllium fluoride), are considered to examine the present study. A spectral collocation method is used to solve the governing equations. The impact of the magnetic field and strength of the internal heating on the instability mechanism is examined. The results show that the MHD fully developed flow stabilizes on increasing the strength of the magnetic field, whereas it destabilizes on increasing the strength of the heat source parameter. The stability of flow also decreases by increasing the Reynolds number. The flow of liquid mercury is more stable in comparison with water-based electrolytes and the Flibe case. The kinetic energy balance shows that the high strength of the magnetic field leads to a significant reduction of the energy amplification of the disturbances. In contrast, the strength of the internal heating acts in a reverse way. Three different types: shear, thermal-shear, and thermal-buoyant, instabilities are observed as a function of Hartmann number for liquid mercury. The type of instability for water-based electrolytes and Flibe is only thermal buoyant. The disturbance flow moves toward the cold wall of the channel on increasing the strength of the magnetic field for all considered fluids, whereas it shifts to the entire channel on increasing the strength of the heat source parameter.

This paper reports the linear stability of laminar magnetohydrodynamic (MHD) mixed convection flow in a differentially heated channel under a transverse magnetic field with the internal heating. Three different electrically conducting fluids, such as liquid mercury, water-based electrolytes, and Flibe (a molten salt mixture of lithium fluoride and beryllium fluoride), are considered to examine the present study. A spectral collocation method is used to solve the governing equations. The impact of the magnetic field and strength of the internal heating on the instability mechanism is examined. The results show that the MHD fully developed flow stabilizes on increasing the strength of the magnetic field, whereas it destabilizes on increasing the strength of the heat source parameter. The stability of flow also decreases by increasing the Reynolds number. The flow of liquid mercury is more stable in comparison with water-based electrolytes and the Flibe case. The kinetic energy balance shows that the high strength of the magnetic field leads to a significant reduction of the energy amplification of the disturbances. In contrast, the strength of the internal heating acts in a reverse way. Three different types: shear, thermal-shear, and thermal-buoyant, instabilities are observed as a function of Hartmann number for liquid mercury. The type of instability for water-based electrolytes and Flibe is only thermal buoyant. The disturbance flow moves toward the cold wall of the channel on increasing the strength of the magnetic field for all considered fluids, whereas it shifts to the entire channel on increasing the strength of the heat source parameter.

Categories: Latest papers in fluid mechanics

### Instability of mixed convection flow in a differentially heated channel under a transverse magnetic field with internal heating

Physics of Fluids, Volume 33, Issue 9, September 2021.

This paper reports the linear stability of laminar magnetohydrodynamic (MHD) mixed convection flow in a differentially heated channel under a transverse magnetic field with the internal heating. Three different electrically conducting fluids, such as liquid mercury, water-based electrolytes, and Flibe (a molten salt mixture of lithium fluoride and beryllium fluoride), are considered to examine the present study. A spectral collocation method is used to solve the governing equations. The impact of the magnetic field and strength of the internal heating on the instability mechanism is examined. The results show that the MHD fully developed flow stabilizes on increasing the strength of the magnetic field, whereas it destabilizes on increasing the strength of the heat source parameter. The stability of flow also decreases by increasing the Reynolds number. The flow of liquid mercury is more stable in comparison with water-based electrolytes and the Flibe case. The kinetic energy balance shows that the high strength of the magnetic field leads to a significant reduction of the energy amplification of the disturbances. In contrast, the strength of the internal heating acts in a reverse way. Three different types: shear, thermal-shear, and thermal-buoyant, instabilities are observed as a function of Hartmann number for liquid mercury. The type of instability for water-based electrolytes and Flibe is only thermal buoyant. The disturbance flow moves toward the cold wall of the channel on increasing the strength of the magnetic field for all considered fluids, whereas it shifts to the entire channel on increasing the strength of the heat source parameter.

This paper reports the linear stability of laminar magnetohydrodynamic (MHD) mixed convection flow in a differentially heated channel under a transverse magnetic field with the internal heating. Three different electrically conducting fluids, such as liquid mercury, water-based electrolytes, and Flibe (a molten salt mixture of lithium fluoride and beryllium fluoride), are considered to examine the present study. A spectral collocation method is used to solve the governing equations. The impact of the magnetic field and strength of the internal heating on the instability mechanism is examined. The results show that the MHD fully developed flow stabilizes on increasing the strength of the magnetic field, whereas it destabilizes on increasing the strength of the heat source parameter. The stability of flow also decreases by increasing the Reynolds number. The flow of liquid mercury is more stable in comparison with water-based electrolytes and the Flibe case. The kinetic energy balance shows that the high strength of the magnetic field leads to a significant reduction of the energy amplification of the disturbances. In contrast, the strength of the internal heating acts in a reverse way. Three different types: shear, thermal-shear, and thermal-buoyant, instabilities are observed as a function of Hartmann number for liquid mercury. The type of instability for water-based electrolytes and Flibe is only thermal buoyant. The disturbance flow moves toward the cold wall of the channel on increasing the strength of the magnetic field for all considered fluids, whereas it shifts to the entire channel on increasing the strength of the heat source parameter.

Categories: Latest papers in fluid mechanics

### Nonuniform heating of a substrate in evaporative lithography

Physics of Fluids, Volume 33, Issue 9, September 2021.

This work is devoted to a method to generate particle cluster assemblies and connected to evaporative lithography. Experiments are carried out using nonuniform evaporation of an isopropanol film containing polystyrene microspheres in a cylindrical cell. The local inhomogeneity of the vapor flux density is achieved by exploiting the temperature gradient. A copper rod is mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient, due in turn to the temperature drop, transfers the particles that were originally at rest at the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and base area of the cluster formed in the central region of the cell is studied. The velocity is measured using particle image velocimetry. A model describing the initial stage of the process is developed. The equations of heat transfer and thermal conductivity are used to define the temperature distribution in the liquid and in the cell. The fluid flow is simulated using the lubrication approximation. The particle distribution is modeled using the convection–diffusion equation. The evaporation flux density is calculated using the Hertz–Knudsen equation. The dependence of the liquid viscosity on the particle concentration is described by Mooney's formula. Numerical results show that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with the increasing temperature. The liquid flow is directed to the heater near the substrate, and it transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The heat flow from the heater affects the geometry of the cluster for two reasons: First, the Marangoni flow velocity depends on the temperature gradient, and second, the decrease in film thickness near the heater depends on the temperature. The results of the simulation are in general agreement with the experimental data.

This work is devoted to a method to generate particle cluster assemblies and connected to evaporative lithography. Experiments are carried out using nonuniform evaporation of an isopropanol film containing polystyrene microspheres in a cylindrical cell. The local inhomogeneity of the vapor flux density is achieved by exploiting the temperature gradient. A copper rod is mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient, due in turn to the temperature drop, transfers the particles that were originally at rest at the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and base area of the cluster formed in the central region of the cell is studied. The velocity is measured using particle image velocimetry. A model describing the initial stage of the process is developed. The equations of heat transfer and thermal conductivity are used to define the temperature distribution in the liquid and in the cell. The fluid flow is simulated using the lubrication approximation. The particle distribution is modeled using the convection–diffusion equation. The evaporation flux density is calculated using the Hertz–Knudsen equation. The dependence of the liquid viscosity on the particle concentration is described by Mooney's formula. Numerical results show that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with the increasing temperature. The liquid flow is directed to the heater near the substrate, and it transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The heat flow from the heater affects the geometry of the cluster for two reasons: First, the Marangoni flow velocity depends on the temperature gradient, and second, the decrease in film thickness near the heater depends on the temperature. The results of the simulation are in general agreement with the experimental data.

Categories: Latest papers in fluid mechanics

### Nonuniform heating of a substrate in evaporative lithography

Physics of Fluids, Volume 33, Issue 9, September 2021.

This work is devoted to a method to generate particle cluster assemblies and connected to evaporative lithography. Experiments are carried out using nonuniform evaporation of an isopropanol film containing polystyrene microspheres in a cylindrical cell. The local inhomogeneity of the vapor flux density is achieved by exploiting the temperature gradient. A copper rod is mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient, due in turn to the temperature drop, transfers the particles that were originally at rest at the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and base area of the cluster formed in the central region of the cell is studied. The velocity is measured using particle image velocimetry. A model describing the initial stage of the process is developed. The equations of heat transfer and thermal conductivity are used to define the temperature distribution in the liquid and in the cell. The fluid flow is simulated using the lubrication approximation. The particle distribution is modeled using the convection–diffusion equation. The evaporation flux density is calculated using the Hertz–Knudsen equation. The dependence of the liquid viscosity on the particle concentration is described by Mooney's formula. Numerical results show that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with the increasing temperature. The liquid flow is directed to the heater near the substrate, and it transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The heat flow from the heater affects the geometry of the cluster for two reasons: First, the Marangoni flow velocity depends on the temperature gradient, and second, the decrease in film thickness near the heater depends on the temperature. The results of the simulation are in general agreement with the experimental data.

This work is devoted to a method to generate particle cluster assemblies and connected to evaporative lithography. Experiments are carried out using nonuniform evaporation of an isopropanol film containing polystyrene microspheres in a cylindrical cell. The local inhomogeneity of the vapor flux density is achieved by exploiting the temperature gradient. A copper rod is mounted in the central part of the bottom of the cell for further heating. The thermocapillary flow resulting from the surface tension gradient, due in turn to the temperature drop, transfers the particles that were originally at rest at the bottom of the cell. The effect of the initial thickness of the liquid layer on the height and base area of the cluster formed in the central region of the cell is studied. The velocity is measured using particle image velocimetry. A model describing the initial stage of the process is developed. The equations of heat transfer and thermal conductivity are used to define the temperature distribution in the liquid and in the cell. The fluid flow is simulated using the lubrication approximation. The particle distribution is modeled using the convection–diffusion equation. The evaporation flux density is calculated using the Hertz–Knudsen equation. The dependence of the liquid viscosity on the particle concentration is described by Mooney's formula. Numerical results show that the liquid film gradually becomes thinner in the central region, as the surface tension decreases with the increasing temperature. The liquid flow is directed to the heater near the substrate, and it transfers the particles to the center of the cell. The volume fraction of the particles increases over time in this region. The heat flow from the heater affects the geometry of the cluster for two reasons: First, the Marangoni flow velocity depends on the temperature gradient, and second, the decrease in film thickness near the heater depends on the temperature. The results of the simulation are in general agreement with the experimental data.

Categories: Latest papers in fluid mechanics

### Extended continuum models for shock waves in CO2

Physics of Fluids, Volume 33, Issue 9, September 2021.

Three continuum models extending the conventional Navier–Stokes–Fourier approach for modeling the shock wave structure in carbon dioxide are developed using the generalized Chapman–Enskog method. Multi-temperature models are based on splitting multiple vibrational relaxation mechanisms into fast and slow processes and introducing vibrational temperatures of various CO2 modes. The one-temperature model takes into account relaxation processes through bulk viscosity and internal thermal conductivity. All developed models are free of limitations introduced by the assumptions of a calorically perfect gas and constant Prandtl number; thermodynamic properties and all transport coefficients are calculated rigorously in each cell of the grid. Simulations are carried out for Mach numbers 3–7; the results are compared with solutions obtained in the frame of other approaches: multi-temperature Euler equations, model kinetic equations, and models with constant Prandtl numbers. The influence of bulk viscosity and Prandtl number on the fluid-dynamic variables, viscous stress, heat flux, and total enthalpy is studied. Bulk viscosity plays an important role in sufficiently rarefied gases under weak deviations from equilibrium; in multi-temperature models, non-equilibrium effects are associated with slow relaxation processes rather than with bulk viscosity. Using a constant Prandtl number yields over-predicted values of the heat flux. Contributions of various energy modes to the total heat flux are evaluated, with emphasis on the compensation of translational–rotational and vibrational energy fluxes.

Three continuum models extending the conventional Navier–Stokes–Fourier approach for modeling the shock wave structure in carbon dioxide are developed using the generalized Chapman–Enskog method. Multi-temperature models are based on splitting multiple vibrational relaxation mechanisms into fast and slow processes and introducing vibrational temperatures of various CO2 modes. The one-temperature model takes into account relaxation processes through bulk viscosity and internal thermal conductivity. All developed models are free of limitations introduced by the assumptions of a calorically perfect gas and constant Prandtl number; thermodynamic properties and all transport coefficients are calculated rigorously in each cell of the grid. Simulations are carried out for Mach numbers 3–7; the results are compared with solutions obtained in the frame of other approaches: multi-temperature Euler equations, model kinetic equations, and models with constant Prandtl numbers. The influence of bulk viscosity and Prandtl number on the fluid-dynamic variables, viscous stress, heat flux, and total enthalpy is studied. Bulk viscosity plays an important role in sufficiently rarefied gases under weak deviations from equilibrium; in multi-temperature models, non-equilibrium effects are associated with slow relaxation processes rather than with bulk viscosity. Using a constant Prandtl number yields over-predicted values of the heat flux. Contributions of various energy modes to the total heat flux are evaluated, with emphasis on the compensation of translational–rotational and vibrational energy fluxes.

Categories: Latest papers in fluid mechanics

### Extended continuum models for shock waves in CO2

Physics of Fluids, Volume 33, Issue 9, September 2021.

Three continuum models extending the conventional Navier–Stokes–Fourier approach for modeling the shock wave structure in carbon dioxide are developed using the generalized Chapman–Enskog method. Multi-temperature models are based on splitting multiple vibrational relaxation mechanisms into fast and slow processes and introducing vibrational temperatures of various CO2 modes. The one-temperature model takes into account relaxation processes through bulk viscosity and internal thermal conductivity. All developed models are free of limitations introduced by the assumptions of a calorically perfect gas and constant Prandtl number; thermodynamic properties and all transport coefficients are calculated rigorously in each cell of the grid. Simulations are carried out for Mach numbers 3–7; the results are compared with solutions obtained in the frame of other approaches: multi-temperature Euler equations, model kinetic equations, and models with constant Prandtl numbers. The influence of bulk viscosity and Prandtl number on the fluid-dynamic variables, viscous stress, heat flux, and total enthalpy is studied. Bulk viscosity plays an important role in sufficiently rarefied gases under weak deviations from equilibrium; in multi-temperature models, non-equilibrium effects are associated with slow relaxation processes rather than with bulk viscosity. Using a constant Prandtl number yields over-predicted values of the heat flux. Contributions of various energy modes to the total heat flux are evaluated, with emphasis on the compensation of translational–rotational and vibrational energy fluxes.

Three continuum models extending the conventional Navier–Stokes–Fourier approach for modeling the shock wave structure in carbon dioxide are developed using the generalized Chapman–Enskog method. Multi-temperature models are based on splitting multiple vibrational relaxation mechanisms into fast and slow processes and introducing vibrational temperatures of various CO2 modes. The one-temperature model takes into account relaxation processes through bulk viscosity and internal thermal conductivity. All developed models are free of limitations introduced by the assumptions of a calorically perfect gas and constant Prandtl number; thermodynamic properties and all transport coefficients are calculated rigorously in each cell of the grid. Simulations are carried out for Mach numbers 3–7; the results are compared with solutions obtained in the frame of other approaches: multi-temperature Euler equations, model kinetic equations, and models with constant Prandtl numbers. The influence of bulk viscosity and Prandtl number on the fluid-dynamic variables, viscous stress, heat flux, and total enthalpy is studied. Bulk viscosity plays an important role in sufficiently rarefied gases under weak deviations from equilibrium; in multi-temperature models, non-equilibrium effects are associated with slow relaxation processes rather than with bulk viscosity. Using a constant Prandtl number yields over-predicted values of the heat flux. Contributions of various energy modes to the total heat flux are evaluated, with emphasis on the compensation of translational–rotational and vibrational energy fluxes.

Categories: Latest papers in fluid mechanics

### Immersed boundary conditions for moving objects in turbulent flows with the lattice-Boltzmann method

Physics of Fluids, Volume 33, Issue 9, September 2021.

An immersed boundary method is coupled to a turbulent wall model and Large Eddy Simulation, within the Lattice-Boltzmann framework. The method is able to handle arbitrarily moving objects immersed in a high Reynolds number flow and to accurately capture the shear layer and near wall effects. We perform a thorough numerical study which validates the numerical method on a set of test-cases of increasing complexity, in order to demonstrate the application of this method to industrial conditions. The robustness and accuracy of the method are assessed first in a static laminar configuration, then in a mobile laminar case, and finally in a static and oscillating turbulent simulation. In all cases, the proposed method shows good results compared to the available data in the literature.

An immersed boundary method is coupled to a turbulent wall model and Large Eddy Simulation, within the Lattice-Boltzmann framework. The method is able to handle arbitrarily moving objects immersed in a high Reynolds number flow and to accurately capture the shear layer and near wall effects. We perform a thorough numerical study which validates the numerical method on a set of test-cases of increasing complexity, in order to demonstrate the application of this method to industrial conditions. The robustness and accuracy of the method are assessed first in a static laminar configuration, then in a mobile laminar case, and finally in a static and oscillating turbulent simulation. In all cases, the proposed method shows good results compared to the available data in the literature.

Categories: Latest papers in fluid mechanics

### Immersed boundary conditions for moving objects in turbulent flows with the lattice-Boltzmann method

Physics of Fluids, Volume 33, Issue 9, September 2021.

An immersed boundary method is coupled to a turbulent wall model and Large Eddy Simulation, within the Lattice-Boltzmann framework. The method is able to handle arbitrarily moving objects immersed in a high Reynolds number flow and to accurately capture the shear layer and near wall effects. We perform a thorough numerical study which validates the numerical method on a set of test-cases of increasing complexity, in order to demonstrate the application of this method to industrial conditions. The robustness and accuracy of the method are assessed first in a static laminar configuration, then in a mobile laminar case, and finally in a static and oscillating turbulent simulation. In all cases, the proposed method shows good results compared to the available data in the literature.

An immersed boundary method is coupled to a turbulent wall model and Large Eddy Simulation, within the Lattice-Boltzmann framework. The method is able to handle arbitrarily moving objects immersed in a high Reynolds number flow and to accurately capture the shear layer and near wall effects. We perform a thorough numerical study which validates the numerical method on a set of test-cases of increasing complexity, in order to demonstrate the application of this method to industrial conditions. The robustness and accuracy of the method are assessed first in a static laminar configuration, then in a mobile laminar case, and finally in a static and oscillating turbulent simulation. In all cases, the proposed method shows good results compared to the available data in the literature.

Categories: Latest papers in fluid mechanics

### Large eddy simulation of tip-leakage cavitating flow using a multiscale cavitation model and investigation on model parameters

Physics of Fluids, Volume 33, Issue 9, September 2021.

For understanding tip-leakage cavitating flow features, the present work aims to implement a multiscale model to comprehensively reproduce the complicated phase structure. The volume of fluid (VOF) interface capturing method is applied to simulate macroscale cavities, while a discrete bubble model using the Lagrangian formulation is newly developed to take the microscale bubbles into account. The Schnerr–Sauer cavitation model is incorporated into the VOF model to calculate the mass transfer rate between phases from the macroscale point of view. For microscale bubbles, the simplified Rayleigh–Plesset equation is adopted to simulate the bubble growing and collapsing stages. An algorithm for coupling the approaches simulating macroscale cavities and microscale bubbles is also implemented to achieve multiscale simulation. Unsteady flow features are simulated using the large eddy simulation approach. The results show that an anti-diffusive compression scheme for the spatial discretization of volume fraction equation is relatively accurate for simulating the tip-leakage cavitating flow. Applying the multiscale model, the tip-leakage cavitating flow features with multiple time and space scales including the formation of glass cavity tube and the transport of bubble clouds can be revealed. Suitable model parameters including the coefficient of saturated pressure, and the bubble evaporation and condensation coefficients are studied.

For understanding tip-leakage cavitating flow features, the present work aims to implement a multiscale model to comprehensively reproduce the complicated phase structure. The volume of fluid (VOF) interface capturing method is applied to simulate macroscale cavities, while a discrete bubble model using the Lagrangian formulation is newly developed to take the microscale bubbles into account. The Schnerr–Sauer cavitation model is incorporated into the VOF model to calculate the mass transfer rate between phases from the macroscale point of view. For microscale bubbles, the simplified Rayleigh–Plesset equation is adopted to simulate the bubble growing and collapsing stages. An algorithm for coupling the approaches simulating macroscale cavities and microscale bubbles is also implemented to achieve multiscale simulation. Unsteady flow features are simulated using the large eddy simulation approach. The results show that an anti-diffusive compression scheme for the spatial discretization of volume fraction equation is relatively accurate for simulating the tip-leakage cavitating flow. Applying the multiscale model, the tip-leakage cavitating flow features with multiple time and space scales including the formation of glass cavity tube and the transport of bubble clouds can be revealed. Suitable model parameters including the coefficient of saturated pressure, and the bubble evaporation and condensation coefficients are studied.

Categories: Latest papers in fluid mechanics

### Large eddy simulation of tip-leakage cavitating flow using a multiscale cavitation model and investigation on model parameters

Physics of Fluids, Volume 33, Issue 9, September 2021.

For understanding tip-leakage cavitating flow features, the present work aims to implement a multiscale model to comprehensively reproduce the complicated phase structure. The volume of fluid (VOF) interface capturing method is applied to simulate macroscale cavities, while a discrete bubble model using the Lagrangian formulation is newly developed to take the microscale bubbles into account. The Schnerr–Sauer cavitation model is incorporated into the VOF model to calculate the mass transfer rate between phases from the macroscale point of view. For microscale bubbles, the simplified Rayleigh–Plesset equation is adopted to simulate the bubble growing and collapsing stages. An algorithm for coupling the approaches simulating macroscale cavities and microscale bubbles is also implemented to achieve multiscale simulation. Unsteady flow features are simulated using the large eddy simulation approach. The results show that an anti-diffusive compression scheme for the spatial discretization of volume fraction equation is relatively accurate for simulating the tip-leakage cavitating flow. Applying the multiscale model, the tip-leakage cavitating flow features with multiple time and space scales including the formation of glass cavity tube and the transport of bubble clouds can be revealed. Suitable model parameters including the coefficient of saturated pressure, and the bubble evaporation and condensation coefficients are studied.

For understanding tip-leakage cavitating flow features, the present work aims to implement a multiscale model to comprehensively reproduce the complicated phase structure. The volume of fluid (VOF) interface capturing method is applied to simulate macroscale cavities, while a discrete bubble model using the Lagrangian formulation is newly developed to take the microscale bubbles into account. The Schnerr–Sauer cavitation model is incorporated into the VOF model to calculate the mass transfer rate between phases from the macroscale point of view. For microscale bubbles, the simplified Rayleigh–Plesset equation is adopted to simulate the bubble growing and collapsing stages. An algorithm for coupling the approaches simulating macroscale cavities and microscale bubbles is also implemented to achieve multiscale simulation. Unsteady flow features are simulated using the large eddy simulation approach. The results show that an anti-diffusive compression scheme for the spatial discretization of volume fraction equation is relatively accurate for simulating the tip-leakage cavitating flow. Applying the multiscale model, the tip-leakage cavitating flow features with multiple time and space scales including the formation of glass cavity tube and the transport of bubble clouds can be revealed. Suitable model parameters including the coefficient of saturated pressure, and the bubble evaporation and condensation coefficients are studied.

Categories: Latest papers in fluid mechanics

### Bluff body uses deep-reinforcement-learning trained active flow control to achieve hydrodynamic stealth

Physics of Fluids, Volume 33, Issue 9, September 2021.

We propose a novel active-flow-control strategy for bluff bodies to hide their hydrodynamic traces, i.e., strong shears and periodically shed vortices, from predators. A group of windward-suction-leeward-blowing (WSLB) actuators are adopted to control the wake of a circular cylinder submerged in a uniform flow. An array of velocity sensors is deployed in the near wake to provide feedback signals. Through the data-driven deep reinforcement learning, effective control strategies are trained for the WSLB actuation to mitigate the cylinder's hydrodynamic signatures. Only a 0.29% deficit in streamwise velocity is detected, which is a 99.5% reduction from the uncontrolled value. The same control strategy is found also to be effective when the cylinder undergoes transverse vortex-induced vibration. The findings from this study can shed some light on the design and operation of underwater structures and robotics to achieve hydrodynamic stealth.

We propose a novel active-flow-control strategy for bluff bodies to hide their hydrodynamic traces, i.e., strong shears and periodically shed vortices, from predators. A group of windward-suction-leeward-blowing (WSLB) actuators are adopted to control the wake of a circular cylinder submerged in a uniform flow. An array of velocity sensors is deployed in the near wake to provide feedback signals. Through the data-driven deep reinforcement learning, effective control strategies are trained for the WSLB actuation to mitigate the cylinder's hydrodynamic signatures. Only a 0.29% deficit in streamwise velocity is detected, which is a 99.5% reduction from the uncontrolled value. The same control strategy is found also to be effective when the cylinder undergoes transverse vortex-induced vibration. The findings from this study can shed some light on the design and operation of underwater structures and robotics to achieve hydrodynamic stealth.

Categories: Latest papers in fluid mechanics

### Bluff body uses deep-reinforcement-learning trained active flow control to achieve hydrodynamic stealth

Physics of Fluids, Volume 33, Issue 9, September 2021.

We propose a novel active-flow-control strategy for bluff bodies to hide their hydrodynamic traces, i.e., strong shears and periodically shed vortices, from predators. A group of windward-suction-leeward-blowing (WSLB) actuators are adopted to control the wake of a circular cylinder submerged in a uniform flow. An array of velocity sensors is deployed in the near wake to provide feedback signals. Through the data-driven deep reinforcement learning, effective control strategies are trained for the WSLB actuation to mitigate the cylinder's hydrodynamic signatures. Only a 0.29% deficit in streamwise velocity is detected, which is a 99.5% reduction from the uncontrolled value. The same control strategy is found also to be effective when the cylinder undergoes transverse vortex-induced vibration. The findings from this study can shed some light on the design and operation of underwater structures and robotics to achieve hydrodynamic stealth.

We propose a novel active-flow-control strategy for bluff bodies to hide their hydrodynamic traces, i.e., strong shears and periodically shed vortices, from predators. A group of windward-suction-leeward-blowing (WSLB) actuators are adopted to control the wake of a circular cylinder submerged in a uniform flow. An array of velocity sensors is deployed in the near wake to provide feedback signals. Through the data-driven deep reinforcement learning, effective control strategies are trained for the WSLB actuation to mitigate the cylinder's hydrodynamic signatures. Only a 0.29% deficit in streamwise velocity is detected, which is a 99.5% reduction from the uncontrolled value. The same control strategy is found also to be effective when the cylinder undergoes transverse vortex-induced vibration. The findings from this study can shed some light on the design and operation of underwater structures and robotics to achieve hydrodynamic stealth.

Categories: Latest papers in fluid mechanics

### Observation of von Kármán vortex street in a droplet breakup

Physics of Fluids, Volume 33, Issue 9, September 2021.

We report the first observation of von Kármán vortex street in a droplet breakup induced by shock waves and high-speed fluid after the shock. To obtain these data, a novel experimental system is used to record the interaction between the droplet and shock wave and the following fluid. Details of flow fields and transients are also presented and discussed. Based on high-speed shadowgraphs, a Strouhal number of 0.28 ± 0.09 with a Reynolds number of 2817 is obtained, which is in good qualitative agreement with earlier experiments on the von Karman vortex street. The results suggest that the vortex-induced vibration may dominate the oscillation in the horizontal direction, which would result in resonance when the frequency of the oscillating flow matches the natural frequency of the droplet, thereby enhancing the deformation and breakup of the droplet. Our data may be useful to benchmark related multiphase flow models or nonlinear theories.

We report the first observation of von Kármán vortex street in a droplet breakup induced by shock waves and high-speed fluid after the shock. To obtain these data, a novel experimental system is used to record the interaction between the droplet and shock wave and the following fluid. Details of flow fields and transients are also presented and discussed. Based on high-speed shadowgraphs, a Strouhal number of 0.28 ± 0.09 with a Reynolds number of 2817 is obtained, which is in good qualitative agreement with earlier experiments on the von Karman vortex street. The results suggest that the vortex-induced vibration may dominate the oscillation in the horizontal direction, which would result in resonance when the frequency of the oscillating flow matches the natural frequency of the droplet, thereby enhancing the deformation and breakup of the droplet. Our data may be useful to benchmark related multiphase flow models or nonlinear theories.

Categories: Latest papers in fluid mechanics