# Physics of Fluids

Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.

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### Hypersonic aerodynamic heating over a flared cone with wavy wall

Physics of Fluids, Volume 31, Issue 5, May 2019.

The influence of a wavy wall on the hypersonic boundary layer transition and the related aerodynamic heating is investigated on a flared cone at a range of unit Reynolds numbers. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, and infrared thermography. The results show that compared to the smooth-wall cone, the wavy-wall one can suppress the second-mode instability to a certain degree and eliminate the local heating spot before transition is completed (denoted as HS). These verify our recent work on aerodynamic heating that HS is caused by the second-mode instability.

The influence of a wavy wall on the hypersonic boundary layer transition and the related aerodynamic heating is investigated on a flared cone at a range of unit Reynolds numbers. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, and infrared thermography. The results show that compared to the smooth-wall cone, the wavy-wall one can suppress the second-mode instability to a certain degree and eliminate the local heating spot before transition is completed (denoted as HS). These verify our recent work on aerodynamic heating that HS is caused by the second-mode instability.

Categories: Latest papers in fluid mechanics

### An experimental study on the effect of swirl number on pollutant formation in propane bluff-body stabilized swirl diffusion flames

Physics of Fluids, Volume 31, Issue 5, May 2019.

The combustion characteristics of propane/air bluff-body stabilized swirl diffusion flames within the turbulent regime are studied experimentally to determine the effect of the swirl number on the flame dynamics and pollutant emissions. The investigated burner consists of a central bluff body with an annulus to introduce the tangential and axial air flows. Results show that in low annulus Reynolds numbers (ReS), the temperature distribution is more affected by the overall equivalence ratio (φo), which is calculated based on the flow rates of the air supplies and the fuel jet. However, by increasing ReS, the impact of swirl number becomes more apparent. Analysis of the combustion products demonstrates a reduction in CO concentration with increasing the geometric swirl number which becomes more evident in higher annulus Reynolds numbers. In addition, the trend of NO emission is strongly analogous to the temperature distribution which is an indication of thermal NO formation. Measurements demonstrate that in lower annulus Reynolds numbers, the dominant factor is the overall equivalence ratio, while with increasing the annulus Reynolds number, the swirl number represents more significance.

The combustion characteristics of propane/air bluff-body stabilized swirl diffusion flames within the turbulent regime are studied experimentally to determine the effect of the swirl number on the flame dynamics and pollutant emissions. The investigated burner consists of a central bluff body with an annulus to introduce the tangential and axial air flows. Results show that in low annulus Reynolds numbers (ReS), the temperature distribution is more affected by the overall equivalence ratio (φo), which is calculated based on the flow rates of the air supplies and the fuel jet. However, by increasing ReS, the impact of swirl number becomes more apparent. Analysis of the combustion products demonstrates a reduction in CO concentration with increasing the geometric swirl number which becomes more evident in higher annulus Reynolds numbers. In addition, the trend of NO emission is strongly analogous to the temperature distribution which is an indication of thermal NO formation. Measurements demonstrate that in lower annulus Reynolds numbers, the dominant factor is the overall equivalence ratio, while with increasing the annulus Reynolds number, the swirl number represents more significance.

Categories: Latest papers in fluid mechanics

### On the suppression and distortion of non-equilibrium fluctuations by transpiration

Physics of Fluids, Volume 31, Issue 5, May 2019.

A fluid in a nonequilibrium state exhibits long-ranged correlations of its hydrodynamic fluctuations. In this article, we examine the effect of a transpiration interface on these correlations—specifically, we consider a dilute gas in a domain bisected by the interface. The system is held in a nonequilibrium steady state by using isothermal walls to impose a temperature gradient. The gas is simulated using both direct simulation Monte Carlo (DSMC) and fluctuating hydrodynamics (FHD). For the FHD simulations, two models are developed for the interface based on master equation and Langevin approaches. For appropriate simulation parameters, good agreement is observed between DSMC and FHD results with the latter showing a significant advantage in computational speed. For each approach, we quantify the effects of transpiration on long-ranged correlations in the hydrodynamic variables. The principal effect of transpiration is a suppression of the correlations, an outcome largely explained by a reduction in the temperature gradient due to the interface. We also observe a distortion of the temperature correlations, specifically the appearance of a new peak located near the interface.

A fluid in a nonequilibrium state exhibits long-ranged correlations of its hydrodynamic fluctuations. In this article, we examine the effect of a transpiration interface on these correlations—specifically, we consider a dilute gas in a domain bisected by the interface. The system is held in a nonequilibrium steady state by using isothermal walls to impose a temperature gradient. The gas is simulated using both direct simulation Monte Carlo (DSMC) and fluctuating hydrodynamics (FHD). For the FHD simulations, two models are developed for the interface based on master equation and Langevin approaches. For appropriate simulation parameters, good agreement is observed between DSMC and FHD results with the latter showing a significant advantage in computational speed. For each approach, we quantify the effects of transpiration on long-ranged correlations in the hydrodynamic variables. The principal effect of transpiration is a suppression of the correlations, an outcome largely explained by a reduction in the temperature gradient due to the interface. We also observe a distortion of the temperature correlations, specifically the appearance of a new peak located near the interface.

Categories: Latest papers in fluid mechanics

### Numerical study of the landslide tsunami in the South China Sea using Herschel-Bulkley rheological theory

Physics of Fluids, Volume 31, Issue 5, May 2019.

The Herschel-Bulkley rheological theory is used to describe the viscoplastic debris landslide flow. The shallow water equations considering the time-dependent deformation of the seafloors are adopted to simulate the generation, propagation, and run-up of the landslide induced tsunami. The one-way coupled method of the landslide induced tsunami is implemented through satisfying the kinematic bottom boundary condition. The 1998 Papua New Guinea landslide tsunami is simulated to validate the numerical model by comparing with measurements. We found that the mechanism of the 1992 Hainan Island tsunami in the South China Sea is due to a submarine landslide by comparing the numerical results between earthquake and landslide. With respect of the Baiyun slide, the effects of remolding rate, initial, and residual yield strength on landslide and tsunami are studied numerically. To distinguish the potential landslide tsunami hazard in the South China Sea, the scenarios of the landslides with the volume of 10, 50, 100, and 200 km3 in the Baiyun slide and 1200 km3 in the Brunei slide are presented. Comparison with the nondeformation model in the near-field illustrates the crucial role of rheological property in the landslide tsunami modeling. Furthermore, the characteristics of the propagation of the landslide tsunami in the South China Sea and coastal hazards are analyzed.

The Herschel-Bulkley rheological theory is used to describe the viscoplastic debris landslide flow. The shallow water equations considering the time-dependent deformation of the seafloors are adopted to simulate the generation, propagation, and run-up of the landslide induced tsunami. The one-way coupled method of the landslide induced tsunami is implemented through satisfying the kinematic bottom boundary condition. The 1998 Papua New Guinea landslide tsunami is simulated to validate the numerical model by comparing with measurements. We found that the mechanism of the 1992 Hainan Island tsunami in the South China Sea is due to a submarine landslide by comparing the numerical results between earthquake and landslide. With respect of the Baiyun slide, the effects of remolding rate, initial, and residual yield strength on landslide and tsunami are studied numerically. To distinguish the potential landslide tsunami hazard in the South China Sea, the scenarios of the landslides with the volume of 10, 50, 100, and 200 km3 in the Baiyun slide and 1200 km3 in the Brunei slide are presented. Comparison with the nondeformation model in the near-field illustrates the crucial role of rheological property in the landslide tsunami modeling. Furthermore, the characteristics of the propagation of the landslide tsunami in the South China Sea and coastal hazards are analyzed.

Categories: Latest papers in fluid mechanics

### Thin reaction zones in constant-density turbulent flows at low Damköhler numbers: Theory and simulations

Physics of Fluids, Volume 31, Issue 5, May 2019.

Propagation of a single-reaction wave in a constant-density turbulent flow is studied by considering reaction rates that depend on the reaction progress variable c in a highly nonlinear manner. Analysis of Direct Numerical Simulation (DNS) data obtained recently from 26 reaction waves characterized by low Damköhler (0.01 < Da < 1) and high Karlovitz (6.5 < Ka < 587) numbers reveals the following trends. First, the ratio of consumption velocity UT to rms turbulent velocity u′ scales as square root of Da in line with Damköhler’s classical hypothesis. Second, the ratio of fully developed turbulent wave thickness to an integral length scale of turbulence decreases with increasing Da and tends to scale with inverse square root of Da, in line with the same hypothesis. Third, contrary to the widely accepted concept of distributed reaction zones, reaction-zone broadening is quite moderate even at Da = 0.01 and Ka = 587. Fourth, contrary to the same concept, UT/u′ is mainly controlled by the reaction-surface area. Fifth, UT/u′ does not vary with the laminar-reaction-zone thickness, provided that Da is constant. To explain the totality of these DNS results, a new theory is developed by (i) exploring the propagation of a molecular mixing layer attached to an infinitely thin reaction sheet in a highly turbulent flow and (ii) hypothesizing that the area of the reaction sheet is controlled by turbulent mixing. This hypothesis is supported by order-of-magnitude estimates and results in the aforementioned Damköhler’s scaling for UT/u′. The theory is also consistent with other aforementioned DNS results and, in particular, explains the weak influence of the laminar-reaction-zone thickness on UT/u′.

Propagation of a single-reaction wave in a constant-density turbulent flow is studied by considering reaction rates that depend on the reaction progress variable c in a highly nonlinear manner. Analysis of Direct Numerical Simulation (DNS) data obtained recently from 26 reaction waves characterized by low Damköhler (0.01 < Da < 1) and high Karlovitz (6.5 < Ka < 587) numbers reveals the following trends. First, the ratio of consumption velocity UT to rms turbulent velocity u′ scales as square root of Da in line with Damköhler’s classical hypothesis. Second, the ratio of fully developed turbulent wave thickness to an integral length scale of turbulence decreases with increasing Da and tends to scale with inverse square root of Da, in line with the same hypothesis. Third, contrary to the widely accepted concept of distributed reaction zones, reaction-zone broadening is quite moderate even at Da = 0.01 and Ka = 587. Fourth, contrary to the same concept, UT/u′ is mainly controlled by the reaction-surface area. Fifth, UT/u′ does not vary with the laminar-reaction-zone thickness, provided that Da is constant. To explain the totality of these DNS results, a new theory is developed by (i) exploring the propagation of a molecular mixing layer attached to an infinitely thin reaction sheet in a highly turbulent flow and (ii) hypothesizing that the area of the reaction sheet is controlled by turbulent mixing. This hypothesis is supported by order-of-magnitude estimates and results in the aforementioned Damköhler’s scaling for UT/u′. The theory is also consistent with other aforementioned DNS results and, in particular, explains the weak influence of the laminar-reaction-zone thickness on UT/u′.

Categories: Latest papers in fluid mechanics

### Evolution of wave pulses in fully nonlinear shallow-water theory

Physics of Fluids, Volume 31, Issue 5, May 2019.

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated, and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage of evolution of initially localized pulses. Analytical results are confirmed by exact numerical solutions of the fully nonlinear shallow-water equations.

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated, and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage of evolution of initially localized pulses. Analytical results are confirmed by exact numerical solutions of the fully nonlinear shallow-water equations.

Categories: Latest papers in fluid mechanics

### Investigation of supersonic turbulent flows over a sphere by fully resolved direct numerical simulation

Physics of Fluids, Volume 31, Issue 5, May 2019.

In this work, a fully resolved direct numerical simulation study of the interaction between supersonic turbulent flow and inertial particle is carried out. For the compressible flow, an eighth-order bandwidth optimization weighted essentially nonoscillatory scheme is used for shock capturing, and the central finite difference scheme is used for the spatial discretization of diffusion terms. The three-dimensional ghost zone immersed boundary method is adopted for solid-fluid interface identification. These numerical schemes are integrated in a direct numerical simulation solver, and its validation is demonstrated by comparing to several benchmark cases. Such a developed method is then used to attack the problem of an upstream supersonic turbulent flow over a spherical particle. Three cases with different inflow turbulence intensities are studied. It is shown that with the turbulence intensity increasing the drag force coefficient presents a smaller relative increase compared to the incompressible situation. Analysis of the bow shock-turbulence interaction is also reported. Similar to the normal shock-turbulence interaction, both the Kolmogorov and Taylor scales decrease after being compressed by the shock. Moreover, both the streamwise and transverse Reynolds stresses have a peak at the shock position. These results indicate the significance of taking the effects of shock into consideration when modeling the modulation of a solid particle to the compressible turbulence.

In this work, a fully resolved direct numerical simulation study of the interaction between supersonic turbulent flow and inertial particle is carried out. For the compressible flow, an eighth-order bandwidth optimization weighted essentially nonoscillatory scheme is used for shock capturing, and the central finite difference scheme is used for the spatial discretization of diffusion terms. The three-dimensional ghost zone immersed boundary method is adopted for solid-fluid interface identification. These numerical schemes are integrated in a direct numerical simulation solver, and its validation is demonstrated by comparing to several benchmark cases. Such a developed method is then used to attack the problem of an upstream supersonic turbulent flow over a spherical particle. Three cases with different inflow turbulence intensities are studied. It is shown that with the turbulence intensity increasing the drag force coefficient presents a smaller relative increase compared to the incompressible situation. Analysis of the bow shock-turbulence interaction is also reported. Similar to the normal shock-turbulence interaction, both the Kolmogorov and Taylor scales decrease after being compressed by the shock. Moreover, both the streamwise and transverse Reynolds stresses have a peak at the shock position. These results indicate the significance of taking the effects of shock into consideration when modeling the modulation of a solid particle to the compressible turbulence.

Categories: Latest papers in fluid mechanics

### Effect of near-wake jet on the lock-in of a freely vibrating square cylinder

Physics of Fluids, Volume 31, Issue 5, May 2019.

We present a numerical study of a freely vibrating square cylinder with steady bleeding at its base side. In particular, we focus on the suppression of vortex-induced vibration (VIV) and the reduction of drag force for the elastically mounted square cylinder at a laminar flow condition via near-wake jet. We examine the base bleeding mechanism in the near-wake region of a square cylinder and its influence over the flow dynamics and the wake characteristics for both stationary (nonlock-in) and freely vibrating (lock-in) conditions. We consider the near-wake jet parameter as a function of the bleed coefficient (Cq), which is the ratio of near-wake jet flow velocity to the freestream velocity and depends on the Reynolds number (Re) based on the diameter of the cylinder. Investigations of the hydrodynamic coefficients and the flow features are carried out for the laminar Re range, namely, Re = 40, 60, 100, and 150. A single dominant frequency peak is observed in the lift coefficient spectrum plot for all the Reynolds numbers considered, but two peaks are observed for Re = 150 at Cq = 0.175 and 0.2. Higher Cq values behave like a splitter plate thereby preventing the interaction of alternating shear layers. The variation of the mean drag is associated with the pressure distribution around the cylinder surface and along the streamwise locations. This leads to a thinner wake width, weaker vortices, and higher vortex shedding frequency as observed earlier in the literature. The sharp spikes of pressure coefficient at the base side of the cylinder are observed for Re ∈ [40, 150] due to the near-wake jet, accounting for the fluctuations of drag force coefficient. We demonstrate the formation of multiple vortices at the wake region due to the near-wake jet from our detailed qualitative analysis. We observe counter-rotating pair of recirculating fluids flanking at the near-wake jet location and examine the recovery of base pressure due to the jet flow. We demonstrate the splitting of big circulation fluid bubble into many smaller counter-rotating fluids due to high-velocity jet flow, resulting into the stabilization of flow profiles in the wake region. We extend this investigation to quantify the effect of the near-wake jet on the two-degree-of-freedom cylinder system at the representative Reynolds number Re = 100 and three mass ratios [math] = 1, 2, and 3. We demonstrate the reduction of peak transverse VIV amplitude by 90% in comparison to the plain cylinder counterpart.

We present a numerical study of a freely vibrating square cylinder with steady bleeding at its base side. In particular, we focus on the suppression of vortex-induced vibration (VIV) and the reduction of drag force for the elastically mounted square cylinder at a laminar flow condition via near-wake jet. We examine the base bleeding mechanism in the near-wake region of a square cylinder and its influence over the flow dynamics and the wake characteristics for both stationary (nonlock-in) and freely vibrating (lock-in) conditions. We consider the near-wake jet parameter as a function of the bleed coefficient (Cq), which is the ratio of near-wake jet flow velocity to the freestream velocity and depends on the Reynolds number (Re) based on the diameter of the cylinder. Investigations of the hydrodynamic coefficients and the flow features are carried out for the laminar Re range, namely, Re = 40, 60, 100, and 150. A single dominant frequency peak is observed in the lift coefficient spectrum plot for all the Reynolds numbers considered, but two peaks are observed for Re = 150 at Cq = 0.175 and 0.2. Higher Cq values behave like a splitter plate thereby preventing the interaction of alternating shear layers. The variation of the mean drag is associated with the pressure distribution around the cylinder surface and along the streamwise locations. This leads to a thinner wake width, weaker vortices, and higher vortex shedding frequency as observed earlier in the literature. The sharp spikes of pressure coefficient at the base side of the cylinder are observed for Re ∈ [40, 150] due to the near-wake jet, accounting for the fluctuations of drag force coefficient. We demonstrate the formation of multiple vortices at the wake region due to the near-wake jet from our detailed qualitative analysis. We observe counter-rotating pair of recirculating fluids flanking at the near-wake jet location and examine the recovery of base pressure due to the jet flow. We demonstrate the splitting of big circulation fluid bubble into many smaller counter-rotating fluids due to high-velocity jet flow, resulting into the stabilization of flow profiles in the wake region. We extend this investigation to quantify the effect of the near-wake jet on the two-degree-of-freedom cylinder system at the representative Reynolds number Re = 100 and three mass ratios [math] = 1, 2, and 3. We demonstrate the reduction of peak transverse VIV amplitude by 90% in comparison to the plain cylinder counterpart.

Categories: Latest papers in fluid mechanics

### Linear stability analysis of a surfactant-laden shear-imposed falling film

Physics of Fluids, Volume 31, Issue 5, May 2019.

A study of the linear stability analysis of a shear-imposed fluid flowing down an inclined plane is performed when the free surface of the fluid is covered by an insoluble surfactant. The purpose is to extend the earlier work [H. H. Wei, “Effect of surfactant on the long-wave instability of a shear-imposed liquid flow down an inclined plane,” Phys. Fluids 17, 012103 (2005)] for disturbances of arbitrary wavenumbers. The Orr-Sommerfeld boundary value problem is formulated and solved numerically based on the Chebyshev spectral collocation method. Two temporal modes, the so-called surface mode and surfactant mode, are detected in the long-wave regime. The surfactant mode becomes unstable when the Péclet number exceeds its critical value. In fact, the instability of the surfactant mode occurs on account for the imposed shear stress. Energy budget analysis predicts that the kinetic energy of the infinitesimal disturbance grows with the imposed shear stress. On the other hand, the numerical results reveal that both surface and surfactant modes can be destabilized by increasing the value of the imposed shear stress. Similarly, it is demonstrated that the shear mode becomes more unstable in the presence of the imposed shear stress. However, it can be stabilized by incorporating the insoluble surfactant at the free surface. Apparently, it seems that inertia does not play any role in the surfactant mode in the moderate Reynolds number regime. Furthermore, the competition between surface and shear modes is discussed.

A study of the linear stability analysis of a shear-imposed fluid flowing down an inclined plane is performed when the free surface of the fluid is covered by an insoluble surfactant. The purpose is to extend the earlier work [H. H. Wei, “Effect of surfactant on the long-wave instability of a shear-imposed liquid flow down an inclined plane,” Phys. Fluids 17, 012103 (2005)] for disturbances of arbitrary wavenumbers. The Orr-Sommerfeld boundary value problem is formulated and solved numerically based on the Chebyshev spectral collocation method. Two temporal modes, the so-called surface mode and surfactant mode, are detected in the long-wave regime. The surfactant mode becomes unstable when the Péclet number exceeds its critical value. In fact, the instability of the surfactant mode occurs on account for the imposed shear stress. Energy budget analysis predicts that the kinetic energy of the infinitesimal disturbance grows with the imposed shear stress. On the other hand, the numerical results reveal that both surface and surfactant modes can be destabilized by increasing the value of the imposed shear stress. Similarly, it is demonstrated that the shear mode becomes more unstable in the presence of the imposed shear stress. However, it can be stabilized by incorporating the insoluble surfactant at the free surface. Apparently, it seems that inertia does not play any role in the surfactant mode in the moderate Reynolds number regime. Furthermore, the competition between surface and shear modes is discussed.

Categories: Latest papers in fluid mechanics

### The drag reduction performance of low Reynolds number pulsating flow in flexible rectangular channels

Physics of Fluids, Volume 31, Issue 5, May 2019.

This work employed theoretical and experimental methods to study the drag reduction performance of flexible channels for low Reynolds number pulsating flow. A novel theoretical model was proposed to describe flow in a flexible rectangular channel. According to the model, the drag reduction of the flexible channel was speculated. Subsequently, experiments were carried out to verify the theoretical results and to illuminate the drag reduction performance of the flexible channel in detail under the impacts of pulsating frequency, nondimensional velocity amplitude, average Reynolds number, and the thickness of the flexible wall. The results indicated that the flexible channel exhibited superior drag reduction performance for pulsating flow as compared to that for steady flow. Meanwhile, the drag reduction rate increased with the increase of pulsating frequency, nondimensional velocity amplitude, and average Reynolds number, and smaller thickness of the flexible wall was in favor of drag reduction at the same flow parameters. Moreover, the current experimental data were utilized to establish a correlation predicting the drag reduction rate of the flexible channel for pulsating flow, which fits 76.4% of 195 data within ±25%.

This work employed theoretical and experimental methods to study the drag reduction performance of flexible channels for low Reynolds number pulsating flow. A novel theoretical model was proposed to describe flow in a flexible rectangular channel. According to the model, the drag reduction of the flexible channel was speculated. Subsequently, experiments were carried out to verify the theoretical results and to illuminate the drag reduction performance of the flexible channel in detail under the impacts of pulsating frequency, nondimensional velocity amplitude, average Reynolds number, and the thickness of the flexible wall. The results indicated that the flexible channel exhibited superior drag reduction performance for pulsating flow as compared to that for steady flow. Meanwhile, the drag reduction rate increased with the increase of pulsating frequency, nondimensional velocity amplitude, and average Reynolds number, and smaller thickness of the flexible wall was in favor of drag reduction at the same flow parameters. Moreover, the current experimental data were utilized to establish a correlation predicting the drag reduction rate of the flexible channel for pulsating flow, which fits 76.4% of 195 data within ±25%.

Categories: Latest papers in fluid mechanics

### Numerical investigation of piston-modal wave resonance in the narrow gap formed by a box in front of a wall

Physics of Fluids, Volume 31, Issue 5, May 2019.

Piston-modal wave resonance between a ship section and a bottom mounted terminal is studied by employing a numerical wave flume based on OpenFOAM® package. A systematic investigation on the piston-modal behavior is performed to characterize the influence of fluid viscosity and flow rotation. Around the resonant frequency, the fluid viscosity and flow rotation not only dissipate the wave amplitude in the narrow gap, but also increase the wave amplitude in the upstream of the box. The dynamic mechanism behind the phenomenon is found to be the interaction between the energy dissipation induced by the fluid vortical flow and energy transformation associated with free surface motion. The increased incident wave amplitude can cause the normalized wave amplitudes and wave forces to deviate more from the potential flow results, while the variation of reflection coefficient is dependent on box-wall geometries. All of these phenomena imply a more significant effect of fluid viscosity and flow rotation with the increase of incident wave amplitude, but the energy dissipation is not the only factor in piston-modal resonance.

Piston-modal wave resonance between a ship section and a bottom mounted terminal is studied by employing a numerical wave flume based on OpenFOAM® package. A systematic investigation on the piston-modal behavior is performed to characterize the influence of fluid viscosity and flow rotation. Around the resonant frequency, the fluid viscosity and flow rotation not only dissipate the wave amplitude in the narrow gap, but also increase the wave amplitude in the upstream of the box. The dynamic mechanism behind the phenomenon is found to be the interaction between the energy dissipation induced by the fluid vortical flow and energy transformation associated with free surface motion. The increased incident wave amplitude can cause the normalized wave amplitudes and wave forces to deviate more from the potential flow results, while the variation of reflection coefficient is dependent on box-wall geometries. All of these phenomena imply a more significant effect of fluid viscosity and flow rotation with the increase of incident wave amplitude, but the energy dissipation is not the only factor in piston-modal resonance.

Categories: Latest papers in fluid mechanics

### Experimental verification of anomalous surface tension temperature dependence at the interface between coexisting liquid-gas phases in magnetic and Stockmayer fluids

Physics of Fluids, Volume 31, Issue 5, May 2019.

Our early experimental investigation has demonstrated the anomalous surface tension temperature dependence σ(T) at the interface between coexisting liquid-gas phases in magnetic fluids that undergo field-induced first-order phase transition. The σ(T) dependence is anomalous because the drops of a liquid phase condensed under the action of the applied magnetic field H at high temperature T2 exhibit larger surface tension σ(T2) > σ(T1) than the drops condensed at low temperature T1 < T2. This study verifies and confirms the results of the previous experimental investigation of σ(T) in magnetic fluids by performing the experiment, which is based on the analysis of the Plateau-Rayleigh instability of a gas-liquid interface in a zero magnetic field. A novel explanation of this phenomenon is given in the framework of the Stockmayer model. The anomalous increase in σ(T) is explained by the increase in particle concentration difference in gas and liquid phases, which can be attributed to the high field intensity H needed to generate the phase transition at high temperature.

Our early experimental investigation has demonstrated the anomalous surface tension temperature dependence σ(T) at the interface between coexisting liquid-gas phases in magnetic fluids that undergo field-induced first-order phase transition. The σ(T) dependence is anomalous because the drops of a liquid phase condensed under the action of the applied magnetic field H at high temperature T2 exhibit larger surface tension σ(T2) > σ(T1) than the drops condensed at low temperature T1 < T2. This study verifies and confirms the results of the previous experimental investigation of σ(T) in magnetic fluids by performing the experiment, which is based on the analysis of the Plateau-Rayleigh instability of a gas-liquid interface in a zero magnetic field. A novel explanation of this phenomenon is given in the framework of the Stockmayer model. The anomalous increase in σ(T) is explained by the increase in particle concentration difference in gas and liquid phases, which can be attributed to the high field intensity H needed to generate the phase transition at high temperature.

Categories: Latest papers in fluid mechanics

### Destruction-of-dissipation and time-scales in wall turbulence

Physics of Fluids, Volume 31, Issue 5, May 2019.

This paper studies the dynamics and scalings of dissipation processes in wall turbulence, focussing on the destruction-of-dissipation tensor [math] (and its halftrace εε), which acts as destruction-by-molecular-viscosity mechanism in the transport equations for the dissipation tensor εij (or its halftrace ε). Budgets of [math]-transport (and εε-transport) are studied for low-Reynolds turbulent plane channel flow. These transport equations also include a destruction-by-molecular-viscosity mechanism, the destruction-of-destruction tensor [math] (or its halftrace [math]), and indeed, recursively, we identify terms [math] defined by correlations of [n + 1]-derivatives which correspond to the destruction mechanism of [math]. Using halftraces ε[n], we may define time-scales, whose study reveals that [math] is approximately equal to the Kolmogorov time-scale. The dependence of the time-scales on the Reynolds number is discussed.

This paper studies the dynamics and scalings of dissipation processes in wall turbulence, focussing on the destruction-of-dissipation tensor [math] (and its halftrace εε), which acts as destruction-by-molecular-viscosity mechanism in the transport equations for the dissipation tensor εij (or its halftrace ε). Budgets of [math]-transport (and εε-transport) are studied for low-Reynolds turbulent plane channel flow. These transport equations also include a destruction-by-molecular-viscosity mechanism, the destruction-of-destruction tensor [math] (or its halftrace [math]), and indeed, recursively, we identify terms [math] defined by correlations of [n + 1]-derivatives which correspond to the destruction mechanism of [math]. Using halftraces ε[n], we may define time-scales, whose study reveals that [math] is approximately equal to the Kolmogorov time-scale. The dependence of the time-scales on the Reynolds number is discussed.

Categories: Latest papers in fluid mechanics

### Numerical study of the material transport in the viscous vortex dipole flow

Physics of Fluids, Volume 31, Issue 5, May 2019.

This paper presents a numerical study of the material transport of Lamb dipole(s) in the two-dimensional viscous flow. We focus on the properties of the rate of strain tensor, which has received less attention in the literature. It is noted that the eigenpairs of the tensor explicitly indicate the strength and direction of material stretching and compressing. The tensor provides a clear map of the material motion regardless of the complexity of the vortical flow. The strain rate field displays a rich structure as it contains five elliptic points and six hyperbolic points. It is interesting to observe that the left elliptic point of the strain rate field bifurcates into two at t > 0. Two kinds of material curves, circular and vertical, are used to illustrate the flow transport. The transport mechanism discussed here can be employed to explore the transport in more complex vortex flows.

This paper presents a numerical study of the material transport of Lamb dipole(s) in the two-dimensional viscous flow. We focus on the properties of the rate of strain tensor, which has received less attention in the literature. It is noted that the eigenpairs of the tensor explicitly indicate the strength and direction of material stretching and compressing. The tensor provides a clear map of the material motion regardless of the complexity of the vortical flow. The strain rate field displays a rich structure as it contains five elliptic points and six hyperbolic points. It is interesting to observe that the left elliptic point of the strain rate field bifurcates into two at t > 0. Two kinds of material curves, circular and vertical, are used to illustrate the flow transport. The transport mechanism discussed here can be employed to explore the transport in more complex vortex flows.

Categories: Latest papers in fluid mechanics

### Shape oscillation of a sessile drop under the effect of high frequency amplitude-modulated magnetic field

Physics of Fluids, Volume 31, Issue 5, May 2019.

The shape oscillation behavior of a sessile mercury drop under the effect of high frequency amplitude-modulated magnetic field (AMMF) is investigated experimentally. It is an effective method to excite the shape oscillation of a liquid metal sessile drop. The high frequency AMMF is generated by a solenoid inductor fed by a specially designed alternating electric current. The surface contour of the sessile drop is observed by a digital camera. At a given modulation frequency and magnetic flux density of the high frequency AMMF, the edge deformations of the drop with azimuthal wave numbers (modes n = 2, 3, 4, 5, 6) were excited. A stability diagram of the shape oscillation of the drop is obtained by analysis of the experimental data. It turns out that when the modulation frequency and magnetic flux density reach a point in the stability diagram which can trigger shape oscillations of the drop of several modes, the shape oscillation of different modes may be seen alternatively.

The shape oscillation behavior of a sessile mercury drop under the effect of high frequency amplitude-modulated magnetic field (AMMF) is investigated experimentally. It is an effective method to excite the shape oscillation of a liquid metal sessile drop. The high frequency AMMF is generated by a solenoid inductor fed by a specially designed alternating electric current. The surface contour of the sessile drop is observed by a digital camera. At a given modulation frequency and magnetic flux density of the high frequency AMMF, the edge deformations of the drop with azimuthal wave numbers (modes n = 2, 3, 4, 5, 6) were excited. A stability diagram of the shape oscillation of the drop is obtained by analysis of the experimental data. It turns out that when the modulation frequency and magnetic flux density reach a point in the stability diagram which can trigger shape oscillations of the drop of several modes, the shape oscillation of different modes may be seen alternatively.

Categories: Latest papers in fluid mechanics

### Numerical investigation of planar shock wave impinging on spherical gas bubble with different densities

Physics of Fluids, Volume 31, Issue 5, May 2019.

The interaction between a planar shock wave and a spherical gas bubble containing sulfur hexafluoride, Refrigerant-22, neon, or helium is studied numerically. Influences of the Atwood number (At) on the evolution of the shock wave and gas bubble are clarified by using high-resolution computational simulations. The results show that the difference in the physical properties between the ambient air and the gas bubble has a significant influence on the evolution of wave pattern and bubble deformation. For the fast/slow configuration (At > 0) in the present study (At = 0.67 and 0.51), the incident shock focuses near the interior right interface to form an outward jet. Besides, the mixedness, average vorticity, and the absolute value of circulation all increase as the Atwood number increases. By contrast, for the slow/fast configuration (At < 0) with At = −0.19 and −0.76, the rotational directions of the vorticities formed at the same position are reversed compared with those in the fast/slow configuration, which induces an inward air jet to impact on the gas bubble from the outside. In addition, the mixedness, average vorticity, and the absolute value of circulation all increase as the Atwood number decreases. Nevertheless, regardless of At > 0 or At < 0, the effective volume of the gas bubble basically decreases when the Atwood number decreases. Hence, on the whole, the Atwood number has a nonmonotonic influence on the evolution of effective volume of gas bubble, mixedness, average vorticity, and circulation simultaneously.

The interaction between a planar shock wave and a spherical gas bubble containing sulfur hexafluoride, Refrigerant-22, neon, or helium is studied numerically. Influences of the Atwood number (At) on the evolution of the shock wave and gas bubble are clarified by using high-resolution computational simulations. The results show that the difference in the physical properties between the ambient air and the gas bubble has a significant influence on the evolution of wave pattern and bubble deformation. For the fast/slow configuration (At > 0) in the present study (At = 0.67 and 0.51), the incident shock focuses near the interior right interface to form an outward jet. Besides, the mixedness, average vorticity, and the absolute value of circulation all increase as the Atwood number increases. By contrast, for the slow/fast configuration (At < 0) with At = −0.19 and −0.76, the rotational directions of the vorticities formed at the same position are reversed compared with those in the fast/slow configuration, which induces an inward air jet to impact on the gas bubble from the outside. In addition, the mixedness, average vorticity, and the absolute value of circulation all increase as the Atwood number decreases. Nevertheless, regardless of At > 0 or At < 0, the effective volume of the gas bubble basically decreases when the Atwood number decreases. Hence, on the whole, the Atwood number has a nonmonotonic influence on the evolution of effective volume of gas bubble, mixedness, average vorticity, and circulation simultaneously.

Categories: Latest papers in fluid mechanics

### Evaluation of oil production potential in fractured porous media

Physics of Fluids, Volume 31, Issue 5, May 2019.

Based on rock samples of tight oil reservoirs in the buried hills of North China, conventional gas flooding and high-speed centrifugal experiments at different pressures were carried out. Combined with nuclear magnetic resonance experiments, an evaluation method of oil production potential in fractured porous media was established to quantitatively study the gas flooding potential of target reservoirs. Results indicated that the “gas fingering phenomenon” is serious in conventional gas flooding experiments of fractured cores even under low pressures because of fractures. With an increase in flooding pressure, the changes of T2 (T2 relaxation time) spectrum and displacement percentage are relatively small, which means that the displacement efficiency has not been improved significantly (the flooding pressure for these three cores increased from 0.014 MPa to 2.6 MPa, with an average increase in displacement percentage of 6.3%). High-speed centrifugation can realize “homogeneous displacement” of the cores and overcome the influence of gas channeling. With an increase in the displacement pressure, the T2 spectrum and percentage of displaced oil varied obviously, and the displacement efficiency improved greatly (the flooding pressure for these three cores increases from 0.014 MPa to 2.6 MPa, with an average percentage of displaced oil being increased to 16.16%). Using the method of this study, 13 cores of the target reservoir were evaluated for gas flooding potential. The percentage of available pores in the target reservoir ranges from 17.64% to 58.54%, with an average of 33.84%. Movable fluid controlled by microthroats in the reservoirs larger than 0.1 mD is about 20%, while that in the reservoirs smaller than 0.1 mD is about 5%. This study indicates that the development of fractures and microfractures controls the physical properties and fluid productivity of reservoirs.

Based on rock samples of tight oil reservoirs in the buried hills of North China, conventional gas flooding and high-speed centrifugal experiments at different pressures were carried out. Combined with nuclear magnetic resonance experiments, an evaluation method of oil production potential in fractured porous media was established to quantitatively study the gas flooding potential of target reservoirs. Results indicated that the “gas fingering phenomenon” is serious in conventional gas flooding experiments of fractured cores even under low pressures because of fractures. With an increase in flooding pressure, the changes of T2 (T2 relaxation time) spectrum and displacement percentage are relatively small, which means that the displacement efficiency has not been improved significantly (the flooding pressure for these three cores increased from 0.014 MPa to 2.6 MPa, with an average increase in displacement percentage of 6.3%). High-speed centrifugation can realize “homogeneous displacement” of the cores and overcome the influence of gas channeling. With an increase in the displacement pressure, the T2 spectrum and percentage of displaced oil varied obviously, and the displacement efficiency improved greatly (the flooding pressure for these three cores increases from 0.014 MPa to 2.6 MPa, with an average percentage of displaced oil being increased to 16.16%). Using the method of this study, 13 cores of the target reservoir were evaluated for gas flooding potential. The percentage of available pores in the target reservoir ranges from 17.64% to 58.54%, with an average of 33.84%. Movable fluid controlled by microthroats in the reservoirs larger than 0.1 mD is about 20%, while that in the reservoirs smaller than 0.1 mD is about 5%. This study indicates that the development of fractures and microfractures controls the physical properties and fluid productivity of reservoirs.

Categories: Latest papers in fluid mechanics

### A numerical study on bubble dynamics in sinusoidal channels

Physics of Fluids, Volume 31, Issue 5, May 2019.

In the present work, we investigate the dynamics of a bubble, rising inside a vertical sinusoidal wavy channel. We carry out a detailed numerical investigation using a dual grid level set method coupled with a finite volume based discretization of the Navier–Stokes equation. A detailed parametric investigation is carried out to identify the fate of the bubble as a function of Reynolds number, Bond number, and the amplitude of the channel wall and represented as a regime map. At a lower Reynolds number (high viscous force), we find negligible wobbling (path instability) in the dynamics of the bubble rise accompanied only with a change in shape of the bubble. However, at a higher Reynolds number, we observe an increase in the wobbling of the bubble due to the lowered viscous effects. Conversely, at a lower Bond number, we predict a stable rise of the bubble due to higher surface tension force. However, with a gradual increase in the Bond number, we predict a periodic oscillation which further tends to instigate the instability in the dynamics. With a further increase in the Bond number, a significant reduction in instability is found unlike a higher Reynolds number with only change in the shape of the bubble. At lower values of Reynolds numbers, Bond numbers, and channel wall amplitudes, the instability is discernible; however, with an increase in the channel wall amplitude, the bubble retains integrity due to higher surface tension force. At a higher Bond number and channel wall amplitude, a multiple breakup in the form of secondary bubbles is observed. We propose a correlation which manifests the average bubble rise velocity and the fluctuating velocity (due to channel waviness) as a function of Reynolds number, Bond number, and channel wall amplitude. Finally, we conclude that the bubble dynamics pertinent to the offset channels with varying amplitudes does not remain the same as that of the symmetric channel.

In the present work, we investigate the dynamics of a bubble, rising inside a vertical sinusoidal wavy channel. We carry out a detailed numerical investigation using a dual grid level set method coupled with a finite volume based discretization of the Navier–Stokes equation. A detailed parametric investigation is carried out to identify the fate of the bubble as a function of Reynolds number, Bond number, and the amplitude of the channel wall and represented as a regime map. At a lower Reynolds number (high viscous force), we find negligible wobbling (path instability) in the dynamics of the bubble rise accompanied only with a change in shape of the bubble. However, at a higher Reynolds number, we observe an increase in the wobbling of the bubble due to the lowered viscous effects. Conversely, at a lower Bond number, we predict a stable rise of the bubble due to higher surface tension force. However, with a gradual increase in the Bond number, we predict a periodic oscillation which further tends to instigate the instability in the dynamics. With a further increase in the Bond number, a significant reduction in instability is found unlike a higher Reynolds number with only change in the shape of the bubble. At lower values of Reynolds numbers, Bond numbers, and channel wall amplitudes, the instability is discernible; however, with an increase in the channel wall amplitude, the bubble retains integrity due to higher surface tension force. At a higher Bond number and channel wall amplitude, a multiple breakup in the form of secondary bubbles is observed. We propose a correlation which manifests the average bubble rise velocity and the fluctuating velocity (due to channel waviness) as a function of Reynolds number, Bond number, and channel wall amplitude. Finally, we conclude that the bubble dynamics pertinent to the offset channels with varying amplitudes does not remain the same as that of the symmetric channel.

Categories: Latest papers in fluid mechanics

### On the role of rarefaction/compression waves in Richtmyer-Meshkov instability with reshock

Physics of Fluids, Volume 31, Issue 5, May 2019.

Richtmyer-Meshkov instability (RMI) with reshock is characterized with the interaction between the mixing zone (MZ) and multiple waves, of which the process has not been fully understood so far. A direct numerical simulation of RMI with reshock, in which the shock initially propagates from a light fluid to a heavy one, is carried out. After the reshock, the MZ is accelerated by rarefaction and compression waves alternatively with decaying strength, during which the mixing zone is accelerated as a whole system and a mean-velocity gradient is evident in the MZ. Although the velocity field is quite complex during rarefaction/compression waves, the scaled profiles of mean volume fraction are not essentially different from those before the first rarefaction wave. A budget analysis reveals that the production of turbulent kinetic energy by the pressure and velocity gradient dominates during the first rarefaction and compression waves. The sign of the pressure-gradient production is opposite to that of the velocity-gradient production, with the amplitude of the former one being larger than that of the latter one. Rarefaction waves contribute to the turbulent motions while compression waves consume turbulence energy. The increment of MZ width is accompanied with formation of large-scale structures. These structures are stretched after the reshock, during the rarefaction waves, and compressed during the compression waves.

Richtmyer-Meshkov instability (RMI) with reshock is characterized with the interaction between the mixing zone (MZ) and multiple waves, of which the process has not been fully understood so far. A direct numerical simulation of RMI with reshock, in which the shock initially propagates from a light fluid to a heavy one, is carried out. After the reshock, the MZ is accelerated by rarefaction and compression waves alternatively with decaying strength, during which the mixing zone is accelerated as a whole system and a mean-velocity gradient is evident in the MZ. Although the velocity field is quite complex during rarefaction/compression waves, the scaled profiles of mean volume fraction are not essentially different from those before the first rarefaction wave. A budget analysis reveals that the production of turbulent kinetic energy by the pressure and velocity gradient dominates during the first rarefaction and compression waves. The sign of the pressure-gradient production is opposite to that of the velocity-gradient production, with the amplitude of the former one being larger than that of the latter one. Rarefaction waves contribute to the turbulent motions while compression waves consume turbulence energy. The increment of MZ width is accompanied with formation of large-scale structures. These structures are stretched after the reshock, during the rarefaction waves, and compressed during the compression waves.

Categories: Latest papers in fluid mechanics

### Characteristics of swirling and precessing flows generated by multiple confined jets

Physics of Fluids, Volume 31, Issue 5, May 2019.

An experimental study is reported of the interaction between multiple isothermal jets within a cylindrical chamber under conditions relevant to a wide range of engineering applications, including the confined swirl combustors, industrial mixers, and concentrated solar thermal devices. The particle image velocimetry technique was used to investigate the swirling and precessing flows generated with four rotationally symmetric inlet pipes at a fixed nozzle Reynolds number of ReD = 10 500 for two configurations of swirl angle (5° and 15°) and two alternative tilt angles (25° and 45°). The measurements reveal three distinctive rotational flow patterns within the external recirculation zone (ERZ) and the central recirculation zone (CRZ) for these configurations. It was found that the mean and root-mean-square flow characteristics of the swirl within the chamber depend strongly on the relative significance of the ERZ and CRZ, with the swirling velocity being higher in the CRZ than that in the ERZ. A precessing vortex core was identified for all experimental conditions considered here, although its significance was less for the cases with a dominant CRZ.

An experimental study is reported of the interaction between multiple isothermal jets within a cylindrical chamber under conditions relevant to a wide range of engineering applications, including the confined swirl combustors, industrial mixers, and concentrated solar thermal devices. The particle image velocimetry technique was used to investigate the swirling and precessing flows generated with four rotationally symmetric inlet pipes at a fixed nozzle Reynolds number of ReD = 10 500 for two configurations of swirl angle (5° and 15°) and two alternative tilt angles (25° and 45°). The measurements reveal three distinctive rotational flow patterns within the external recirculation zone (ERZ) and the central recirculation zone (CRZ) for these configurations. It was found that the mean and root-mean-square flow characteristics of the swirl within the chamber depend strongly on the relative significance of the ERZ and CRZ, with the swirling velocity being higher in the CRZ than that in the ERZ. A precessing vortex core was identified for all experimental conditions considered here, although its significance was less for the cases with a dominant CRZ.

Categories: Latest papers in fluid mechanics