# Latest papers in fluid mechanics

### Experimental study of droplet shedding on laser-patterned substrates

Physics of Fluids, Volume 31, Issue 12, December 2019.

An experimental study was performed to investigate the dynamics of droplet shedding under the effect of various shear flow speeds on a laser micromachined surface with superhydrophobic properties. To account for the effect of liquid properties on droplet shedding, four different liquids were used in these sets of experiments, namely, distilled water, ethylene glycol, propylene glycol, and glycerol. The wetting length of the liquid droplets was measured based on the air shear speed, and three different regimes were observed based on the critical Weber and Ohnesorge numbers. In the first regime, where the Weber and Ohnesorge numbers are low, droplets deform with slight movement or rotation without detachment from the surface. Under the second regime, where the Weber number is relatively high and the Ohnesorge number is low, droplets deform and detach from the surface, and then subsequent breakup may occur. The variation of droplet detachment time with the Weber and Ohnesorge numbers is further discussed in this paper. In the third regime, where the Ohnesorge number is high, there is no droplet detachment nor are rivulets formed. Finally, empirical correlations are developed to predict the droplet behavior on laser-patterned surfaces under the effect of shear flow. This work can be used as a baseline to study the droplet dynamics on a superhydrophobic surface in cases where temperature changes the liquid properties.

An experimental study was performed to investigate the dynamics of droplet shedding under the effect of various shear flow speeds on a laser micromachined surface with superhydrophobic properties. To account for the effect of liquid properties on droplet shedding, four different liquids were used in these sets of experiments, namely, distilled water, ethylene glycol, propylene glycol, and glycerol. The wetting length of the liquid droplets was measured based on the air shear speed, and three different regimes were observed based on the critical Weber and Ohnesorge numbers. In the first regime, where the Weber and Ohnesorge numbers are low, droplets deform with slight movement or rotation without detachment from the surface. Under the second regime, where the Weber number is relatively high and the Ohnesorge number is low, droplets deform and detach from the surface, and then subsequent breakup may occur. The variation of droplet detachment time with the Weber and Ohnesorge numbers is further discussed in this paper. In the third regime, where the Ohnesorge number is high, there is no droplet detachment nor are rivulets formed. Finally, empirical correlations are developed to predict the droplet behavior on laser-patterned surfaces under the effect of shear flow. This work can be used as a baseline to study the droplet dynamics on a superhydrophobic surface in cases where temperature changes the liquid properties.

Categories: Latest papers in fluid mechanics

### Dynamic and energy analysis of coalescence-induced self-propelled jumping of binary unequal-sized droplets

Physics of Fluids, Volume 31, Issue 12, December 2019.

The coalescence-induced self-propelled droplet jumping on superhydrophobic surfaces has a large number of potential applications such as enhancement of condensation heat transfer, self-cleaning, and anti-icing, which becomes a current hotspot. At present, most of the research studies focus on the self-propelled jumping of two identical droplets; however, the jumping induced by unequal-sized droplets is much closer to actuality. In this paper, the coalescence-induced self-propelled jumping of binary unequal-sized droplets is simulated and all energy terms are studied. The normalized liquid bridge width induced by unequal-sized droplets is a function of the square root of the normalized time, and the maximum jumping velocity is a function of the radius ratio as well. The maximum jumping velocity descends with the decrease in the radius ratio and contact angle, and the critical radius ratio shows an upward trend with the decrease in the contact angle. Furthermore, all energy terms decline with the decrease in the radius ratio. The effective energy conversion rate of binary equal-sized jumping is very low, less than 3% in our results. This rate of binary unequal-sized jumping further reduces due to the existence of asymmetric flow. This work helps for a better understanding of the characteristics of coalescence-induced self-propelled droplet jumping.

The coalescence-induced self-propelled droplet jumping on superhydrophobic surfaces has a large number of potential applications such as enhancement of condensation heat transfer, self-cleaning, and anti-icing, which becomes a current hotspot. At present, most of the research studies focus on the self-propelled jumping of two identical droplets; however, the jumping induced by unequal-sized droplets is much closer to actuality. In this paper, the coalescence-induced self-propelled jumping of binary unequal-sized droplets is simulated and all energy terms are studied. The normalized liquid bridge width induced by unequal-sized droplets is a function of the square root of the normalized time, and the maximum jumping velocity is a function of the radius ratio as well. The maximum jumping velocity descends with the decrease in the radius ratio and contact angle, and the critical radius ratio shows an upward trend with the decrease in the contact angle. Furthermore, all energy terms decline with the decrease in the radius ratio. The effective energy conversion rate of binary equal-sized jumping is very low, less than 3% in our results. This rate of binary unequal-sized jumping further reduces due to the existence of asymmetric flow. This work helps for a better understanding of the characteristics of coalescence-induced self-propelled droplet jumping.

Categories: Latest papers in fluid mechanics

### Stabilization of the boundary layer by streamwise control

Physics of Fluids, Volume 31, Issue 12, December 2019.

In this paper, the effect of a special active control on the Blasius boundary layer is investigated with the Orr-Sommerfeld and the Reynolds-Orr energy equations. The control moves the wall in the streamwise direction proportional to the fluctuating wall shear stress which was proposed by Józsa et al. [“Active and passive in-plane wall fluctuations in turbulent channel flows,” J. Fluid Mech. 866, 689–720 (2019)]. Our results showed that the negative proportional parameters destabilize the flow, while the positive values lead to a contradictory outcome. According to the Orr-Sommerfeld equation, with the right choice of the parameter, the critical Reynolds number can be significantly increased. At the same time, the Reynolds-Orr equation predicts that any streamwise movement of the wall proportional to the wall shear stress slightly destabilizes the flow.

In this paper, the effect of a special active control on the Blasius boundary layer is investigated with the Orr-Sommerfeld and the Reynolds-Orr energy equations. The control moves the wall in the streamwise direction proportional to the fluctuating wall shear stress which was proposed by Józsa et al. [“Active and passive in-plane wall fluctuations in turbulent channel flows,” J. Fluid Mech. 866, 689–720 (2019)]. Our results showed that the negative proportional parameters destabilize the flow, while the positive values lead to a contradictory outcome. According to the Orr-Sommerfeld equation, with the right choice of the parameter, the critical Reynolds number can be significantly increased. At the same time, the Reynolds-Orr equation predicts that any streamwise movement of the wall proportional to the wall shear stress slightly destabilizes the flow.

Categories: Latest papers in fluid mechanics

### Large scale dynamics of a high Reynolds number axisymmetric separating/reattaching flow

Physics of Fluids, Volume 31, Issue 12, December 2019.

A numerical study is conducted to unveil the large scale dynamics of a high Reynolds number axisymmetric separating/reattaching flow at M∞ = 0.7. The numerical simulation allows us to acquire a high rate sampled unsteady volumetric dataset. This huge amount of spatial and temporal information is exploited in the Fourier space to visualize for the first time in physical space and at such a high Reynolds number (ReD = 1.2 × 106) the statistical signature of the helical structure related to the antisymmetric mode (m = 1) at StD = 0.18. The main hydrodynamic mechanisms are identified through the spatial distribution of the most energetic frequencies, i.e., StD = 0.18 and StD ≥ 3.0 corresponding to the vortex-shedding and Kelvin-Helmholtz instability phenomena, respectively. In particular, the dynamics related to the dimensionless shedding frequency is shown to become dominant for 0.35 ≤ x/D ≤ 0.75 in the whole radial direction as it passes through the shear layer. The spatial distribution of the coherence function for the most significant modes as well as a three-dimensional Fourier decomposition suggests the global features of the flow mechanisms. More specifically, the novelty of this study lies in the evidence of the flow dynamics through the use of cross-correlation maps plotted with a frequency selection guided by the characteristic Strouhal number formerly identified in a local manner in the flow field or at the wall. Moreover and for the first time, the understanding of the scales at stake is supported both by a Fourier analysis and a dynamic mode decomposition in the complete three-dimensional space surrounding the afterbody zone.

A numerical study is conducted to unveil the large scale dynamics of a high Reynolds number axisymmetric separating/reattaching flow at M∞ = 0.7. The numerical simulation allows us to acquire a high rate sampled unsteady volumetric dataset. This huge amount of spatial and temporal information is exploited in the Fourier space to visualize for the first time in physical space and at such a high Reynolds number (ReD = 1.2 × 106) the statistical signature of the helical structure related to the antisymmetric mode (m = 1) at StD = 0.18. The main hydrodynamic mechanisms are identified through the spatial distribution of the most energetic frequencies, i.e., StD = 0.18 and StD ≥ 3.0 corresponding to the vortex-shedding and Kelvin-Helmholtz instability phenomena, respectively. In particular, the dynamics related to the dimensionless shedding frequency is shown to become dominant for 0.35 ≤ x/D ≤ 0.75 in the whole radial direction as it passes through the shear layer. The spatial distribution of the coherence function for the most significant modes as well as a three-dimensional Fourier decomposition suggests the global features of the flow mechanisms. More specifically, the novelty of this study lies in the evidence of the flow dynamics through the use of cross-correlation maps plotted with a frequency selection guided by the characteristic Strouhal number formerly identified in a local manner in the flow field or at the wall. Moreover and for the first time, the understanding of the scales at stake is supported both by a Fourier analysis and a dynamic mode decomposition in the complete three-dimensional space surrounding the afterbody zone.

Categories: Latest papers in fluid mechanics

### Memory embedded non-intrusive reduced order modeling of non-ergodic flows

Physics of Fluids, Volume 31, Issue 12, December 2019.

Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two, but the novel nonintrusive approach presented in this study is an attempt at taking all three into account effectively compared to their traditional counterparts. Based on dimensionality reduction using proper orthogonal decomposition (POD), we introduce a long short-term memory neural network architecture together with a principal interval decomposition (PID) framework as an enabler to account for localized modal deformation. As an effective partitioning tool for breaking the Kolmogorov barrier, our PID framework, therefore, can be considered a key element in the accurate reduced order modeling of convective flows. Our applications for convection-dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations demonstrate that the proposed approach yields significantly more accurate predictions than the POD-Galerkin method and could be a key enabler toward near real-time predictions of unsteady flows.

Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two, but the novel nonintrusive approach presented in this study is an attempt at taking all three into account effectively compared to their traditional counterparts. Based on dimensionality reduction using proper orthogonal decomposition (POD), we introduce a long short-term memory neural network architecture together with a principal interval decomposition (PID) framework as an enabler to account for localized modal deformation. As an effective partitioning tool for breaking the Kolmogorov barrier, our PID framework, therefore, can be considered a key element in the accurate reduced order modeling of convective flows. Our applications for convection-dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations demonstrate that the proposed approach yields significantly more accurate predictions than the POD-Galerkin method and could be a key enabler toward near real-time predictions of unsteady flows.

Categories: Latest papers in fluid mechanics

### Aspect ratio studies on insect wings

Physics of Fluids, Volume 31, Issue 12, December 2019.

The wing aspect ratio (AR), that is, the ratio of the wingspan to the mean wing chord, is the most important geometrical parameter describing an insect wing. While studies have shown that a change in AR affects the flow structure as well as the aerodynamic force components on wings, the reasons behind the wide variety of aspect ratios observed in nature remain underexplored. Further to this, motivated by the developments in micro-air vehicles (MAVs), determining an optimum AR is important for their efficient operation. While the effects on flow structure appear to be, at least superficially, broadly consistent across different studies, the effects on aerodynamic forces have been more strongly debated. Indeed, the considerable variation of force coefficients with AR in different studies suggests different optimal ARs. To help explain this, recent studies have pointed out the coupled effects of AR with other parameters. Specifically, the use of Reynolds and Rossby numbers based on alternative scalings helps to at least partially decouple the effects of AR and also to reconcile previous conflicting trends. This brief review presents an overview of previous studies on aspect-ratio effects of insectlike wings summarizing the main findings. The suggested alternative scalings of Reynolds and Rossby numbers, using the wingspan as the characteristic length, may be useful in aiding the selection of the optimal aspect ratios for MAVs in the future.

The wing aspect ratio (AR), that is, the ratio of the wingspan to the mean wing chord, is the most important geometrical parameter describing an insect wing. While studies have shown that a change in AR affects the flow structure as well as the aerodynamic force components on wings, the reasons behind the wide variety of aspect ratios observed in nature remain underexplored. Further to this, motivated by the developments in micro-air vehicles (MAVs), determining an optimum AR is important for their efficient operation. While the effects on flow structure appear to be, at least superficially, broadly consistent across different studies, the effects on aerodynamic forces have been more strongly debated. Indeed, the considerable variation of force coefficients with AR in different studies suggests different optimal ARs. To help explain this, recent studies have pointed out the coupled effects of AR with other parameters. Specifically, the use of Reynolds and Rossby numbers based on alternative scalings helps to at least partially decouple the effects of AR and also to reconcile previous conflicting trends. This brief review presents an overview of previous studies on aspect-ratio effects of insectlike wings summarizing the main findings. The suggested alternative scalings of Reynolds and Rossby numbers, using the wingspan as the characteristic length, may be useful in aiding the selection of the optimal aspect ratios for MAVs in the future.

Categories: Latest papers in fluid mechanics

### Solute release from an elastic capsule flowing through a microfluidic channel constriction

Physics of Fluids, Volume 31, Issue 12, December 2019.

In recent years, microfluidic channels with narrow constrictions are extensively proposed as a new but excellent possibility for advanced delivery technologies based on either natural or artificial capsules. To better design and optimize these technologies, it is essential and helpful to fully understand the releasing behavior of the encapsulated solute from capsules under various flow conditions which, however, remains an unsolved fundamental problem due to its complexity. To facilitate studies in this area, we develop a numerical methodology for the simulation of solute release from an elastic capsule flowing through a microfluidic channel constriction, in which the tension-dependent permeability of the membrane is appropriately modeled. Using this model, we find that the release of the encapsulated solute during the capsule’s passage through the constriction is enhanced with the increase in the capillary number and constriction length or the decrease in the constriction width. On the other hand, a large variation in the channel height, which is generally larger than the capsule diameter, generates little effect on the released amount of the solute. We reveal that the effects of the capillary number and constriction geometry on the solute release are generally attributed to their influence on the capsule deformation. Our numerical results provide a reasonable explanation for previous experimental observations on the effects of constriction geometry and flow rate on the delivery efficiency of cell-squeezing delivery systems. Therefore, we believe these new insights and our numerical methodology could be useful for the design and optimization of microfluidic devices for capsule-squeezing delivery technologies.

In recent years, microfluidic channels with narrow constrictions are extensively proposed as a new but excellent possibility for advanced delivery technologies based on either natural or artificial capsules. To better design and optimize these technologies, it is essential and helpful to fully understand the releasing behavior of the encapsulated solute from capsules under various flow conditions which, however, remains an unsolved fundamental problem due to its complexity. To facilitate studies in this area, we develop a numerical methodology for the simulation of solute release from an elastic capsule flowing through a microfluidic channel constriction, in which the tension-dependent permeability of the membrane is appropriately modeled. Using this model, we find that the release of the encapsulated solute during the capsule’s passage through the constriction is enhanced with the increase in the capillary number and constriction length or the decrease in the constriction width. On the other hand, a large variation in the channel height, which is generally larger than the capsule diameter, generates little effect on the released amount of the solute. We reveal that the effects of the capillary number and constriction geometry on the solute release are generally attributed to their influence on the capsule deformation. Our numerical results provide a reasonable explanation for previous experimental observations on the effects of constriction geometry and flow rate on the delivery efficiency of cell-squeezing delivery systems. Therefore, we believe these new insights and our numerical methodology could be useful for the design and optimization of microfluidic devices for capsule-squeezing delivery technologies.

Categories: Latest papers in fluid mechanics

### Detection of the thermoacoustic combustion instabilities of a slot burner based on a diagonal-wise recurrence quantification

Physics of Fluids, Volume 31, Issue 12, December 2019.

This paper presents a nonlinear time-series analysis of the thermoacoustic instabilities of an experimental slot burner. The main objective was the calculation of indexes capable of detecting in advance the combustion instabilities by gradually increasing the flow Reynolds number of the pilot burner. A chaotic analysis based on diagonalwise measurements of the recurrence plots was performed on the basis of which the following indexes were calculated: the τ-recurrence rate index RRτ, the τ-determinism index DETτ, the τ-average diagonal line length index Lτ, and the τ-entropy index sτ. A quantification carried out by means of the standard deviation σ and mean values μ of the diagonalwise measurements showed that the aforementioned indexes were successfully able to sort all cases under analysis mainly into two groups: the first three cases that correspond to the stable regime named “Combustion Noise” and the remaining cases that were associated with the unstable regime called “Combustion Instability.” Additionally, the particle image velocimetry optical method was applied in order to compute a new index based on the velocity fields. The results showed that the index Vh, based on the local heights of the velocity profiles of the central flame, was also capable of detecting the same two groups previously identified by the nonlinear analysis. Nevertheless, the most sensitive indexes were the indexes [math], [math], and [math] since these indexes were able to detect the transition between the combustion noise and combustion instability regimes. Therefore, the present results proved that the proposed five indexes were effective precursors in order to detect in advance the combustion instabilities.

This paper presents a nonlinear time-series analysis of the thermoacoustic instabilities of an experimental slot burner. The main objective was the calculation of indexes capable of detecting in advance the combustion instabilities by gradually increasing the flow Reynolds number of the pilot burner. A chaotic analysis based on diagonalwise measurements of the recurrence plots was performed on the basis of which the following indexes were calculated: the τ-recurrence rate index RRτ, the τ-determinism index DETτ, the τ-average diagonal line length index Lτ, and the τ-entropy index sτ. A quantification carried out by means of the standard deviation σ and mean values μ of the diagonalwise measurements showed that the aforementioned indexes were successfully able to sort all cases under analysis mainly into two groups: the first three cases that correspond to the stable regime named “Combustion Noise” and the remaining cases that were associated with the unstable regime called “Combustion Instability.” Additionally, the particle image velocimetry optical method was applied in order to compute a new index based on the velocity fields. The results showed that the index Vh, based on the local heights of the velocity profiles of the central flame, was also capable of detecting the same two groups previously identified by the nonlinear analysis. Nevertheless, the most sensitive indexes were the indexes [math], [math], and [math] since these indexes were able to detect the transition between the combustion noise and combustion instability regimes. Therefore, the present results proved that the proposed five indexes were effective precursors in order to detect in advance the combustion instabilities.

Categories: Latest papers in fluid mechanics

### Tracking disturbances in transitional and turbulent flows: Coherent structures

Physics of Fluids, Volume 31, Issue 12, December 2019.

Tracking transitional and turbulent flows requires methods other than the classical techniques, which capture coherent structures via locating pressure minima, after the disturbance field has evolved to late-transitional and turbulent flow stages. Keeping it in mind, transition to turbulence of zero pressure gradient flow is studied, following two routes of excitation, by solving the three-dimensional Navier-Stokes equation in derived variable formulation, with vorticity as one of the dependent variables. For such flows, disturbance structures should be traced from the receptivity to the coherent structure stage for the fully developed turbulent flow. The coherent structures in turbulent flows are identified by the Q- and λ2-criteria, based on the occurrence of pressure minima at the vortex cores. In the proposed study here, the zero pressure gradient boundary layer is excited (i) at the wall with a monochromatic source and (ii) causing transition to turbulence, by a convecting vortex in the free stream. The main aim here is to trace the incipient disturbances from the onset to the turbulent state in terms of physical quantities, such as the disturbance mechanical energy introduced by Sengupta et al. [“Vortex-induced instability of an incompressible wall-bounded shear layer,” J. Fluid Mech. 493, 277–286 (2003)] and disturbance enstrophy transport equation, as proposed by Sengupta et al. [“An enstrophy-based linear and nonlinear receptivity theory,” Phys. Fluids 30(5), 054106 (2018)]. Such methods are capable of tracing disturbance structures from the onset to the evolved stage. We compare these methods with Q- and λ2-criteria to trace disturbance evolution.

Tracking transitional and turbulent flows requires methods other than the classical techniques, which capture coherent structures via locating pressure minima, after the disturbance field has evolved to late-transitional and turbulent flow stages. Keeping it in mind, transition to turbulence of zero pressure gradient flow is studied, following two routes of excitation, by solving the three-dimensional Navier-Stokes equation in derived variable formulation, with vorticity as one of the dependent variables. For such flows, disturbance structures should be traced from the receptivity to the coherent structure stage for the fully developed turbulent flow. The coherent structures in turbulent flows are identified by the Q- and λ2-criteria, based on the occurrence of pressure minima at the vortex cores. In the proposed study here, the zero pressure gradient boundary layer is excited (i) at the wall with a monochromatic source and (ii) causing transition to turbulence, by a convecting vortex in the free stream. The main aim here is to trace the incipient disturbances from the onset to the turbulent state in terms of physical quantities, such as the disturbance mechanical energy introduced by Sengupta et al. [“Vortex-induced instability of an incompressible wall-bounded shear layer,” J. Fluid Mech. 493, 277–286 (2003)] and disturbance enstrophy transport equation, as proposed by Sengupta et al. [“An enstrophy-based linear and nonlinear receptivity theory,” Phys. Fluids 30(5), 054106 (2018)]. Such methods are capable of tracing disturbance structures from the onset to the evolved stage. We compare these methods with Q- and λ2-criteria to trace disturbance evolution.

Categories: Latest papers in fluid mechanics

### Probing fluid torque with a hydrodynamical trap: Rotation of chiral particles levitating in a turbulent jet

Physics of Fluids, Volume 31, Issue 12, December 2019.

A vertical turbulent jet is used to trap chiral particles. The particles are maintained in levitation and a stationary rotation regime is observed. The model particles used are composed of a sphere and a helical tail. The rotating performance of the particles is investigated as a function of the length and the twisting of their tails. In addition, the flow field around a spherical particle trapped in the jet is characterized by a 3D-particle tracking velocimetry technique. This flow characterization is used to compute the near-field velocity around a captured particle and to predict the rotation reported for the different geometries tested.

A vertical turbulent jet is used to trap chiral particles. The particles are maintained in levitation and a stationary rotation regime is observed. The model particles used are composed of a sphere and a helical tail. The rotating performance of the particles is investigated as a function of the length and the twisting of their tails. In addition, the flow field around a spherical particle trapped in the jet is characterized by a 3D-particle tracking velocimetry technique. This flow characterization is used to compute the near-field velocity around a captured particle and to predict the rotation reported for the different geometries tested.

Categories: Latest papers in fluid mechanics

### Numerical investigation on evolutionary characteristics of the leading-edge vortex induced by flapping caudal fin

Physics of Fluids, Volume 31, Issue 12, December 2019.

The caudal fin of a fish is one of the main determinants of various maneuvering motions. In this paper, the evolutionary characteristics of the leading-edge vortex (LEV) induced by three kinds of forked caudal fins with different chord lengths are studied. Numerical results show that the emergence and development of the LEV are directly related to the distribution law of the angle of attack (AoA) caused by the leading-edge configuration. However, when adopting a fixed motion mode, any temporal evolution in the AoA of the leading-edge location is determined by the distance between the leading-edge location and the pitching axis, the combined effects of heaving and pitching motions, and the Strouhal number. An increase in the chord length enhances the strength of the LEV, leading to more vortex-augmented thrust. Nonetheless, the chord length of a forked caudal fin cannot be extended indefinitely as this will alter the temporal evolution of the AoA and seriously delay the generation of the LEV. Our research is helpful in understanding how the locomotor force is derived from the motion of the caudal fin and provides a reference for biomimetic roboticists to choose appropriate propellers for underwater vehicles.

The caudal fin of a fish is one of the main determinants of various maneuvering motions. In this paper, the evolutionary characteristics of the leading-edge vortex (LEV) induced by three kinds of forked caudal fins with different chord lengths are studied. Numerical results show that the emergence and development of the LEV are directly related to the distribution law of the angle of attack (AoA) caused by the leading-edge configuration. However, when adopting a fixed motion mode, any temporal evolution in the AoA of the leading-edge location is determined by the distance between the leading-edge location and the pitching axis, the combined effects of heaving and pitching motions, and the Strouhal number. An increase in the chord length enhances the strength of the LEV, leading to more vortex-augmented thrust. Nonetheless, the chord length of a forked caudal fin cannot be extended indefinitely as this will alter the temporal evolution of the AoA and seriously delay the generation of the LEV. Our research is helpful in understanding how the locomotor force is derived from the motion of the caudal fin and provides a reference for biomimetic roboticists to choose appropriate propellers for underwater vehicles.

Categories: Latest papers in fluid mechanics

### Subgrid-scale model for large-eddy simulation of transition and turbulence in compressible flows

Physics of Fluids, Volume 31, Issue 12, December 2019.

This article focuses on a subgrid-scale (SGS) eddy viscosity model based on helicity which is derived from our previous research [Yu et al., “Subgrid-scale eddy viscosity model for helical turbulence,” Phys. Fluids 25, 095101 (2013)] for large-eddy simulation of transition and turbulence in compressible flows. Based on the character of the compressible boundary layer over a flat plate, we obtain from theoretical analysis that this model can automatically distinguish laminar flow and turbulence and can also simulate turbulence well. Meanwhile, an a priori test using direct numerical simulation (DNS) data of a spatially developing flat-plate boundary layer at Ma = 2.25 shows that the helicity model can clearly differentiate laminar, transitional, and turbulent regions. Comparing the numerical simulation results with DNS and other SGS models in the spatially developing boundary-layer over a flat plate, we find that the suggested model could precisely predict the onset of transition, transition peak, skin-friction coefficient, mean velocity profile, mean temperature profile, and turbulence intensities. In the case of a compression ramp, the model can well simulate the bypass-type transition, the separated and reattached points, and the size of the separation bubble in the corner region. Furthermore, the prominent advantage of the proposed model can predict transitional flow exactly with no explicit filtering or dynamic procedure.

This article focuses on a subgrid-scale (SGS) eddy viscosity model based on helicity which is derived from our previous research [Yu et al., “Subgrid-scale eddy viscosity model for helical turbulence,” Phys. Fluids 25, 095101 (2013)] for large-eddy simulation of transition and turbulence in compressible flows. Based on the character of the compressible boundary layer over a flat plate, we obtain from theoretical analysis that this model can automatically distinguish laminar flow and turbulence and can also simulate turbulence well. Meanwhile, an a priori test using direct numerical simulation (DNS) data of a spatially developing flat-plate boundary layer at Ma = 2.25 shows that the helicity model can clearly differentiate laminar, transitional, and turbulent regions. Comparing the numerical simulation results with DNS and other SGS models in the spatially developing boundary-layer over a flat plate, we find that the suggested model could precisely predict the onset of transition, transition peak, skin-friction coefficient, mean velocity profile, mean temperature profile, and turbulence intensities. In the case of a compression ramp, the model can well simulate the bypass-type transition, the separated and reattached points, and the size of the separation bubble in the corner region. Furthermore, the prominent advantage of the proposed model can predict transitional flow exactly with no explicit filtering or dynamic procedure.

Categories: Latest papers in fluid mechanics

### Triple points and sign of circulation

Physics of Fluids, Volume 31, Issue 12, December 2019.

Interaction of multiple shock waves generally produces a contact discontinuity whose circulation has previously been analyzed using “thermodynamic” arguments based on the Hugoniot relations across the shocks. We focus on “kinematic” techniques that avoid assumptions about the equation of state, using only jump relations for the conservation of mass and momentum but not energy. We give a new short proof for the nonexistence of pure (no contact) triple shocks, recovering a result of Serre. For Mach reflection with a zero-circulation but nonzero-density-jump contact, we show that the incident shock must be normal. Nonexistence without contacts generalizes to two or more incident shocks if we assume that all shocks are compressive. The sign of circulation across the contact has previously been controlled with entropy arguments, showing that the post-Mach-stem velocity is generally smaller. We give a kinematic proof assuming compressive shocks and another condition, such as backward incident shocks, or a weak form of the Lax condition. We also show that for 2 + 2 and higher interactions (multiple “upper” shocks with clockwise flow meeting multiple “lower” shocks with counterclockwise flow in a single point), the circulation sign can generally not be controlled. For γ-law pressure, we show that 2 + 2 interactions without contacts must be either symmetric or antisymmetric, with symmetry favored at low Mach numbers and low shock strengths. For full potential flow instead of the Euler equations, we surprisingly find, contrary to folklore and prior results for other models, that pure triple shocks without contacts are possible, even for γ-law pressure with 1 < γ < 3.

Interaction of multiple shock waves generally produces a contact discontinuity whose circulation has previously been analyzed using “thermodynamic” arguments based on the Hugoniot relations across the shocks. We focus on “kinematic” techniques that avoid assumptions about the equation of state, using only jump relations for the conservation of mass and momentum but not energy. We give a new short proof for the nonexistence of pure (no contact) triple shocks, recovering a result of Serre. For Mach reflection with a zero-circulation but nonzero-density-jump contact, we show that the incident shock must be normal. Nonexistence without contacts generalizes to two or more incident shocks if we assume that all shocks are compressive. The sign of circulation across the contact has previously been controlled with entropy arguments, showing that the post-Mach-stem velocity is generally smaller. We give a kinematic proof assuming compressive shocks and another condition, such as backward incident shocks, or a weak form of the Lax condition. We also show that for 2 + 2 and higher interactions (multiple “upper” shocks with clockwise flow meeting multiple “lower” shocks with counterclockwise flow in a single point), the circulation sign can generally not be controlled. For γ-law pressure, we show that 2 + 2 interactions without contacts must be either symmetric or antisymmetric, with symmetry favored at low Mach numbers and low shock strengths. For full potential flow instead of the Euler equations, we surprisingly find, contrary to folklore and prior results for other models, that pure triple shocks without contacts are possible, even for γ-law pressure with 1 < γ < 3.

Categories: Latest papers in fluid mechanics

### Sensing the turbulent large-scale motions with their wall signature

Physics of Fluids, Volume PACT2019, Issue 1, December 2019.

This study assesses the capability of extended proper orthogonal decomposition (EPOD) and convolutional neural networks (CNNs) to reconstruct large-scale and very-large-scale motions (LSMs and VLSMs respectively) employing wall-shear-stress measurements in wall-bounded turbulent flows. Both techniques are used to reconstruct the instantaneous LSM evolution in the flow field as a combination of proper orthogonal decomposition (POD) modes, employing a limited set of instantaneous wall-shear-stress measurements. Due to the dominance of nonlinear effects, only CNNs provide satisfying results. Being able to account for nonlinearities in the flow, CNNs are shown to perform significantly better than EPOD in terms of both instantaneous flow-field estimation and turbulent-statistics reconstruction. CNNs are able to provide a more effective reconstruction performance employing more POD modes at larger distances from the wall and employing lower wall-measurement resolutions. Furthermore, the capability of tackling nonlinear features of CNNs results in estimation capabilities that are weakly dependent on the distance from the wall.

This study assesses the capability of extended proper orthogonal decomposition (EPOD) and convolutional neural networks (CNNs) to reconstruct large-scale and very-large-scale motions (LSMs and VLSMs respectively) employing wall-shear-stress measurements in wall-bounded turbulent flows. Both techniques are used to reconstruct the instantaneous LSM evolution in the flow field as a combination of proper orthogonal decomposition (POD) modes, employing a limited set of instantaneous wall-shear-stress measurements. Due to the dominance of nonlinear effects, only CNNs provide satisfying results. Being able to account for nonlinearities in the flow, CNNs are shown to perform significantly better than EPOD in terms of both instantaneous flow-field estimation and turbulent-statistics reconstruction. CNNs are able to provide a more effective reconstruction performance employing more POD modes at larger distances from the wall and employing lower wall-measurement resolutions. Furthermore, the capability of tackling nonlinear features of CNNs results in estimation capabilities that are weakly dependent on the distance from the wall.

Categories: Latest papers in fluid mechanics

### Revisiting Thomson equation for accurate modeling of pore scale thermodynamics of hydrocarbon solvents

Physics of Fluids, Volume 31, Issue 12, December 2019.

As stated by the classical Thomson equation, the pore scale thermodynamics of a solvent is different from bulk conditions, being critically controlled by capillary characteristics. This equation shows that the boiling point temperatures decrease remarkably as the pore size becomes smaller, after a threshold value. This paper experimentally investigates this phenomenon for hydrocarbon solvents and compares the results with the values, obtained from the Thomson equation, to test its applicability in modeling heavy-oil recovery by solvents under nonisothermal conditions. As an initial step, the boiling point temperatures of two single-component solvents (heptane and decane) were measured by saturating Hele-Shaw type cells with variable apertures (ranging from 0.04 mm to 5 mm) and monitoring the boiling process. One experiment was run with a thickness of 12 mm to represent the bulk case. As the aperture (pore size) became smaller, the boiling point temperature decreased. For example, the measured boiling temperatures of heptane and decane were approximately 58 °C and 107 °C for the aperture values less than 0.15 mm, which were considerably lower than the “bulk” values (around 40%). In the next step, the same experiments were repeated using micromodels, representing porous media. Using the Thomson equation, the boiling points of the selected liquids were mathematically computed and compared with the experimental results from Hele-Shaw and micromodel experiments. Finally, modifications to the Thomson equation and alternative formulations were suggested.

As stated by the classical Thomson equation, the pore scale thermodynamics of a solvent is different from bulk conditions, being critically controlled by capillary characteristics. This equation shows that the boiling point temperatures decrease remarkably as the pore size becomes smaller, after a threshold value. This paper experimentally investigates this phenomenon for hydrocarbon solvents and compares the results with the values, obtained from the Thomson equation, to test its applicability in modeling heavy-oil recovery by solvents under nonisothermal conditions. As an initial step, the boiling point temperatures of two single-component solvents (heptane and decane) were measured by saturating Hele-Shaw type cells with variable apertures (ranging from 0.04 mm to 5 mm) and monitoring the boiling process. One experiment was run with a thickness of 12 mm to represent the bulk case. As the aperture (pore size) became smaller, the boiling point temperature decreased. For example, the measured boiling temperatures of heptane and decane were approximately 58 °C and 107 °C for the aperture values less than 0.15 mm, which were considerably lower than the “bulk” values (around 40%). In the next step, the same experiments were repeated using micromodels, representing porous media. Using the Thomson equation, the boiling points of the selected liquids were mathematically computed and compared with the experimental results from Hele-Shaw and micromodel experiments. Finally, modifications to the Thomson equation and alternative formulations were suggested.

Categories: Latest papers in fluid mechanics

### Deconstructing electrode pore network to learn transport distortion

Physics of Fluids, Volume 31, Issue 12, December 2019.

The central premise of porous electrodes is to make more surface area available for reactions. However, the convoluted pore network of such reactors exacerbates the transport of reacting species. Tortuosity is a measure of such transport distortion and is conventionally expressed in terms of porosity (the fraction of electrode volume occupied by liquid-filled pores). Such an approach is overly simplistic and falls short of accounting for spatial variabilities characteristic of electrode samples. These networks are defined by multiple features such as size distribution, connectivity, and pore morphology, none of which are explicitly considered in a porosity based interpretation, thus limiting predictability. We propose a recourse using a two-point correlation function that deconstructs the pore network into its essential attributes. Such a quantitative representation is mapped to the transport response of these networks. Given the explicit treatment of pore network geometry, this approach provides a consistent treatment of three-dimensionalities such as inhomogeneity and anisotropy. Three-dimensional (3D) tomograms of Li-ion battery electrodes are studied to characterize the efficacy of the proposed approach. The proposed approach is applicable to abstracting effective properties related to different transport modes in porous fluid networks.

The central premise of porous electrodes is to make more surface area available for reactions. However, the convoluted pore network of such reactors exacerbates the transport of reacting species. Tortuosity is a measure of such transport distortion and is conventionally expressed in terms of porosity (the fraction of electrode volume occupied by liquid-filled pores). Such an approach is overly simplistic and falls short of accounting for spatial variabilities characteristic of electrode samples. These networks are defined by multiple features such as size distribution, connectivity, and pore morphology, none of which are explicitly considered in a porosity based interpretation, thus limiting predictability. We propose a recourse using a two-point correlation function that deconstructs the pore network into its essential attributes. Such a quantitative representation is mapped to the transport response of these networks. Given the explicit treatment of pore network geometry, this approach provides a consistent treatment of three-dimensionalities such as inhomogeneity and anisotropy. Three-dimensional (3D) tomograms of Li-ion battery electrodes are studied to characterize the efficacy of the proposed approach. The proposed approach is applicable to abstracting effective properties related to different transport modes in porous fluid networks.

Categories: Latest papers in fluid mechanics

### Laser-induced control of a cavity bubble behind a sinking sphere in water entry: Dependency on the surface temperature and impact velocity

Physics of Fluids, Volume 31, Issue 12, December 2019.

We investigate the effect of continuous-wave laser irradiation on the cavity evolution behind a sphere in water entry. By tuning the irradiation time, the surface temperature (Ts) of the sphere before the impact varies in 105–355 °C. We change the radius and impact velocity of the sphere, by which both the shallow and deep seals are considered. Compared to the reference case (the sphere was roughened to have a cavity initially), we find that the cavity expands or shrinks depending on Ts. Overall, for all cases, the cavity bubble expands to the maximum size and shrinks steeply with increasing Ts. At higher Ts, the cavity is destroyed significantly, even smaller than the reference case. However, the detailed interaction between the cavity and laser-induced cavitation bubbles is quite different. In a shallow-seal case, nucleate boiling occurs on the sphere surface and vapor bubbles merge into the cavity, resulting in the expansion of the cavity. At a highly subcooled condition, on the other hand, the vapor bubble collapses into microbubbles as soon as it contacts water, resulting in the cavity reduction. As the impact speed increases (for a deep-seal condition), the flux of entrained air becomes dominant and the stage of cavity expansion is quite narrow. As Ts increases, the heated cavity collapses into microbubbles and almost 90% is destroyed. Finally, we investigate the effects of modified cavity on hydrodynamic forces on the sphere. While the temporal variation of hydrodynamic forces is complex, the drag reduction over 40% is achieved.

We investigate the effect of continuous-wave laser irradiation on the cavity evolution behind a sphere in water entry. By tuning the irradiation time, the surface temperature (Ts) of the sphere before the impact varies in 105–355 °C. We change the radius and impact velocity of the sphere, by which both the shallow and deep seals are considered. Compared to the reference case (the sphere was roughened to have a cavity initially), we find that the cavity expands or shrinks depending on Ts. Overall, for all cases, the cavity bubble expands to the maximum size and shrinks steeply with increasing Ts. At higher Ts, the cavity is destroyed significantly, even smaller than the reference case. However, the detailed interaction between the cavity and laser-induced cavitation bubbles is quite different. In a shallow-seal case, nucleate boiling occurs on the sphere surface and vapor bubbles merge into the cavity, resulting in the expansion of the cavity. At a highly subcooled condition, on the other hand, the vapor bubble collapses into microbubbles as soon as it contacts water, resulting in the cavity reduction. As the impact speed increases (for a deep-seal condition), the flux of entrained air becomes dominant and the stage of cavity expansion is quite narrow. As Ts increases, the heated cavity collapses into microbubbles and almost 90% is destroyed. Finally, we investigate the effects of modified cavity on hydrodynamic forces on the sphere. While the temporal variation of hydrodynamic forces is complex, the drag reduction over 40% is achieved.

Categories: Latest papers in fluid mechanics

### Numerical simulation of film instability over low wettability surfaces through lubrication theory

Physics of Fluids, Volume 31, Issue 12, December 2019.

A computational study of thin liquid films over a solid surface is reported. The lubrication equation is numerically solved using an in-house code, which implements the finite volume method. Small slope approximation is abandoned, and a more accurate model for capillary pressure estimation is presented, allowing us to correctly investigate higher contact angles, when compared to the maximum value allowed by small slope approximation. Disjoining pressure is used for modeling substrate wettability. The in-house solver is first validated: a 1D flowing film driven by gravity is simulated and the disjoining pressure model is verified for contact angles up to 60°; replicating literature experimental investigations, a uniform film covering an inclined plate is perturbed, inducing the generation of a large dry patch; rivulet buildup is simulated; and the numerical results are compared with fully 3D computations found in the literature and verified with analytical evidences. Then, a film flowing over an inclined plate bounded by lateral walls, which is a complex configuration commonly used for studying liquid behavior in structured packing, is investigated and relevant parameters are reported.

A computational study of thin liquid films over a solid surface is reported. The lubrication equation is numerically solved using an in-house code, which implements the finite volume method. Small slope approximation is abandoned, and a more accurate model for capillary pressure estimation is presented, allowing us to correctly investigate higher contact angles, when compared to the maximum value allowed by small slope approximation. Disjoining pressure is used for modeling substrate wettability. The in-house solver is first validated: a 1D flowing film driven by gravity is simulated and the disjoining pressure model is verified for contact angles up to 60°; replicating literature experimental investigations, a uniform film covering an inclined plate is perturbed, inducing the generation of a large dry patch; rivulet buildup is simulated; and the numerical results are compared with fully 3D computations found in the literature and verified with analytical evidences. Then, a film flowing over an inclined plate bounded by lateral walls, which is a complex configuration commonly used for studying liquid behavior in structured packing, is investigated and relevant parameters are reported.

Categories: Latest papers in fluid mechanics

### M-shaped flame dynamics

Physics of Fluids, Volume 31, Issue 12, December 2019.

This article deals with the dynamics of a cylindrical bluff-body-stabilized M-shaped premixed flame at low flow rates. A comparative analysis with classical conical flames was performed. The velocities and flame front field dynamics were studied with the use of numerical methods. It was shown that the processes under the investigation are similar to those in a conical flame. The flame front is deformed by moving Kelvin–Helmholtz vortices along the front. It was found that M-shaped flame tips perform in-phase low-frequency oscillations in both vertical and horizontal directions as opposed to the conical one. It was also found that fuel enrichment does not affect the frequency of the flicker as compared to the classical conical flame. A number of experiments have shown that vertical displacement amplitude in M-shaped flame is approximately 3.5 times smaller than in a conical one at the same flow rate. An explanation of this phenomenon is the fact that a part of the energy under compression goes to the horizontal displacement of the front.

This article deals with the dynamics of a cylindrical bluff-body-stabilized M-shaped premixed flame at low flow rates. A comparative analysis with classical conical flames was performed. The velocities and flame front field dynamics were studied with the use of numerical methods. It was shown that the processes under the investigation are similar to those in a conical flame. The flame front is deformed by moving Kelvin–Helmholtz vortices along the front. It was found that M-shaped flame tips perform in-phase low-frequency oscillations in both vertical and horizontal directions as opposed to the conical one. It was also found that fuel enrichment does not affect the frequency of the flicker as compared to the classical conical flame. A number of experiments have shown that vertical displacement amplitude in M-shaped flame is approximately 3.5 times smaller than in a conical one at the same flow rate. An explanation of this phenomenon is the fact that a part of the energy under compression goes to the horizontal displacement of the front.

Categories: Latest papers in fluid mechanics

### Sensing the turbulent large-scale motions with their wall signature

Physics of Fluids, Volume 31, Issue 12, December 2019.

This study assesses the capability of extended proper orthogonal decomposition (EPOD) and convolutional neural networks (CNNs) to reconstruct large-scale and very-large-scale motions (LSMs and VLSMs respectively) employing wall-shear-stress measurements in wall-bounded turbulent flows. Both techniques are used to reconstruct the instantaneous LSM evolution in the flow field as a combination of proper orthogonal decomposition (POD) modes, employing a limited set of instantaneous wall-shear-stress measurements. Due to the dominance of nonlinear effects, only CNNs provide satisfying results. Being able to account for nonlinearities in the flow, CNNs are shown to perform significantly better than EPOD in terms of both instantaneous flow-field estimation and turbulent-statistics reconstruction. CNNs are able to provide a more effective reconstruction performance employing more POD modes at larger distances from the wall and employing lower wall-measurement resolutions. Furthermore, the capability of tackling nonlinear features of CNNs results in estimation capabilities that are weakly dependent on the distance from the wall.

This study assesses the capability of extended proper orthogonal decomposition (EPOD) and convolutional neural networks (CNNs) to reconstruct large-scale and very-large-scale motions (LSMs and VLSMs respectively) employing wall-shear-stress measurements in wall-bounded turbulent flows. Both techniques are used to reconstruct the instantaneous LSM evolution in the flow field as a combination of proper orthogonal decomposition (POD) modes, employing a limited set of instantaneous wall-shear-stress measurements. Due to the dominance of nonlinear effects, only CNNs provide satisfying results. Being able to account for nonlinearities in the flow, CNNs are shown to perform significantly better than EPOD in terms of both instantaneous flow-field estimation and turbulent-statistics reconstruction. CNNs are able to provide a more effective reconstruction performance employing more POD modes at larger distances from the wall and employing lower wall-measurement resolutions. Furthermore, the capability of tackling nonlinear features of CNNs results in estimation capabilities that are weakly dependent on the distance from the wall.

Categories: Latest papers in fluid mechanics