# Physics of Fluids

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

*Updated:*16 hours 19 min ago

### Effect of periodic perturbations on the turbulence statistics in a backward-facing step flow

Physics of Fluids, Volume 32, Issue 7, July 2020.

Turbulence budget for natural and periodically perturbed backward-facing step flows was studied using particle image velocimetry data, aiming to provide more evidence for the mechanisms of the turbulence production under perturbation. The flow has a Reynolds number of 9630 based on the step height. A synthetic jet actuator deployed at the step corner was used to perturb the flow with a wide range of parameters including different frequencies and amplitudes. The results show that the sizes of the turbulence production terms are enhanced with efficiency when flow is perturbed at a frequency near the shear layer mode frequency. The enhancement is associated with vortical structures produced by the perturbation. The length scale of the structures is similar to the step height. In contrast, the low-frequency perturbation (with a frequency which is 25% of the shear layer mode frequency) has less impact on the turbulence production despite the large amplitude vertical flapping motion of the whole shear layer and large increases in the streamwise Reynolds normal stress occur.

Turbulence budget for natural and periodically perturbed backward-facing step flows was studied using particle image velocimetry data, aiming to provide more evidence for the mechanisms of the turbulence production under perturbation. The flow has a Reynolds number of 9630 based on the step height. A synthetic jet actuator deployed at the step corner was used to perturb the flow with a wide range of parameters including different frequencies and amplitudes. The results show that the sizes of the turbulence production terms are enhanced with efficiency when flow is perturbed at a frequency near the shear layer mode frequency. The enhancement is associated with vortical structures produced by the perturbation. The length scale of the structures is similar to the step height. In contrast, the low-frequency perturbation (with a frequency which is 25% of the shear layer mode frequency) has less impact on the turbulence production despite the large amplitude vertical flapping motion of the whole shear layer and large increases in the streamwise Reynolds normal stress occur.

Categories: Latest papers in fluid mechanics

### The analytic description of a stationary flow over a narrow obstacle

Physics of Fluids, Volume 32, Issue 7, July 2020.

A stationary flow over a narrow obstacle is considered. Though the problem seems rather simple, it appears that it is not amenable to standard shallow water theory. Therefore, the flow is modeled by the Euler equations with the natural boundary conditions, including the flow at infinity given as the constant solution in shallow water theory. Then, the model is approximated by the linearized Euler equations, which are transformed into a problem of finding an analytic velocity satisfying rather unusual boundary conditions. This velocity is then determined with the help of a Fourier transform and used to calculate some approximate flow contours.

A stationary flow over a narrow obstacle is considered. Though the problem seems rather simple, it appears that it is not amenable to standard shallow water theory. Therefore, the flow is modeled by the Euler equations with the natural boundary conditions, including the flow at infinity given as the constant solution in shallow water theory. Then, the model is approximated by the linearized Euler equations, which are transformed into a problem of finding an analytic velocity satisfying rather unusual boundary conditions. This velocity is then determined with the help of a Fourier transform and used to calculate some approximate flow contours.

Categories: Latest papers in fluid mechanics

### Investigation and parameterization of transition shielding in roughness-disturbed boundary layer with direct numerical simulations

Physics of Fluids, Volume 32, Issue 7, July 2020.

Roughness-induced transition control is a key technology for aircraft design, and associated research is useful in practical applications as well as for understanding the mechanism of the roughness-induced transition. One practical approach involves the “shielding effect,” whereby the roughness-induced transition is shielded by smaller pockets of surrounding roughness. In this paper, we investigate the shielding effect of a two-dimensional downstream strip in the boundary layer disturbed by discrete smooth-edged roughness and focus on the shielding strip height kss and the distance between the two areas of roughness xss. Our results indicate that downstream shielding delays the transition by weakening the strongest streamwise vortices in the middle of the wake, thus inhibiting the “lift-up” effect that induces growth in the disturbance. The main mechanisms for reducing the streamwise vorticity are (a) enhanced dissipation of the streamwise vorticity and (b) conversion of streamwise vorticity into more stable spanwise vorticity. The strip suppresses the separation zone behind the roughness, thus affecting the receptivity process and reducing the initial disturbance. However, the strip strengthens other streamwise vortices in the wake. When kss exceeds a critical value, vortices closer to the wall will induce stronger lift-up than those in the middle of the wake, resulting in an earlier transition. Analysis of xss shows a simpler trend, whereby the onset position of the transition moves upstream as xss increases. This is because the shielding strip weakens the streamwise vortices earlier and the separation zone becomes smaller as the strip moves closer to the discrete roughness patch.

Roughness-induced transition control is a key technology for aircraft design, and associated research is useful in practical applications as well as for understanding the mechanism of the roughness-induced transition. One practical approach involves the “shielding effect,” whereby the roughness-induced transition is shielded by smaller pockets of surrounding roughness. In this paper, we investigate the shielding effect of a two-dimensional downstream strip in the boundary layer disturbed by discrete smooth-edged roughness and focus on the shielding strip height kss and the distance between the two areas of roughness xss. Our results indicate that downstream shielding delays the transition by weakening the strongest streamwise vortices in the middle of the wake, thus inhibiting the “lift-up” effect that induces growth in the disturbance. The main mechanisms for reducing the streamwise vorticity are (a) enhanced dissipation of the streamwise vorticity and (b) conversion of streamwise vorticity into more stable spanwise vorticity. The strip suppresses the separation zone behind the roughness, thus affecting the receptivity process and reducing the initial disturbance. However, the strip strengthens other streamwise vortices in the wake. When kss exceeds a critical value, vortices closer to the wall will induce stronger lift-up than those in the middle of the wake, resulting in an earlier transition. Analysis of xss shows a simpler trend, whereby the onset position of the transition moves upstream as xss increases. This is because the shielding strip weakens the streamwise vortices earlier and the separation zone becomes smaller as the strip moves closer to the discrete roughness patch.

Categories: Latest papers in fluid mechanics

### How the circulation and axial velocity deficit in Batchelor vortices affect their disturbance growth?

Physics of Fluids, Volume 32, Issue 7, July 2020.

In this study, inviscid linear stability theory is used to investigate the compressibility effects of Batchelor vortices. The growth rates are obtained from asymptotic analysis with large wavenumbers, and it is shown that the growth of disturbances is affected largely by both the Mach number and the axial velocity deficit. From the maximum growth rates for various base flow conditions, the growth properties of Batchelor vortices are summarized reasonably by using a convective Mach number based on two relative Mach numbers for three-dimensional disturbances. In addition, the ratio of the circulation and velocity deficit at the maximum growth rate is closely related to the growth rate as a function of the convective Mach number because the correlation between the ratio and the growth rate is high when the Mach number is less than unity. Therefore, the compressibility effects, which are expressed as the relation between the growth property and the convective Mach number, are estimated simply from only the base flows (circulation and velocity deficit) in Batchelor vortices.

In this study, inviscid linear stability theory is used to investigate the compressibility effects of Batchelor vortices. The growth rates are obtained from asymptotic analysis with large wavenumbers, and it is shown that the growth of disturbances is affected largely by both the Mach number and the axial velocity deficit. From the maximum growth rates for various base flow conditions, the growth properties of Batchelor vortices are summarized reasonably by using a convective Mach number based on two relative Mach numbers for three-dimensional disturbances. In addition, the ratio of the circulation and velocity deficit at the maximum growth rate is closely related to the growth rate as a function of the convective Mach number because the correlation between the ratio and the growth rate is high when the Mach number is less than unity. Therefore, the compressibility effects, which are expressed as the relation between the growth property and the convective Mach number, are estimated simply from only the base flows (circulation and velocity deficit) in Batchelor vortices.

Categories: Latest papers in fluid mechanics

### Laboratory verification of the buoyancy dependence of the carrying flow in a Maxey–Riley theory for inertial ocean dynamics

Physics of Fluids, Volume 32, Issue 7, July 2020.

We present results from laboratory experiments conducted in an air–water stream flume facility that provide controlled observational support for the buoyancy dependence of the drag-induced carrying flow velocity in a recent Maxey–Riley theory for inertial particle motion in the ocean.

We present results from laboratory experiments conducted in an air–water stream flume facility that provide controlled observational support for the buoyancy dependence of the drag-induced carrying flow velocity in a recent Maxey–Riley theory for inertial particle motion in the ocean.

Categories: Latest papers in fluid mechanics

### Vortex core formation in a Francis turbine during transient operation from best efficiency point to high load

Physics of Fluids, Volume 32, Issue 7, July 2020.

This study presents the experiments performed on a model Francis turbine during load acceptance from best efficiency point to high load conditions. The Reynolds number varies from 7.3 × 105 to 9.0 × 105 during the measurement. A vortex core is generally observed in the draft tube of the Francis turbine at high load operation. However, the mechanism of formation of the core is not yet highlighted using an experimental flow-field study. This paper illustrates the mechanism involved in the formation of the vortex core using synchronized velocity and pressure measurements. The measurements are performed on a model Francis turbine. A fully developed vortex core is observed in the draft tube at high load operation, and the formation of the core originates with the formation of the stagnant, reverse, and recirculating flow regions during load acceptance. The vortex core rotates in the direction opposite to the runner rotation. The axial velocity profiles are observed to change from jet-like to wake-like during the formation of a vortex core. The large velocity gradients represent the sharp transition in the flow around the center axis of the draft tube. The severe pressure fluctuations corresponding to rotor–stator interaction and pressure waves are observed in the draft tube and vaneless space.

This study presents the experiments performed on a model Francis turbine during load acceptance from best efficiency point to high load conditions. The Reynolds number varies from 7.3 × 105 to 9.0 × 105 during the measurement. A vortex core is generally observed in the draft tube of the Francis turbine at high load operation. However, the mechanism of formation of the core is not yet highlighted using an experimental flow-field study. This paper illustrates the mechanism involved in the formation of the vortex core using synchronized velocity and pressure measurements. The measurements are performed on a model Francis turbine. A fully developed vortex core is observed in the draft tube at high load operation, and the formation of the core originates with the formation of the stagnant, reverse, and recirculating flow regions during load acceptance. The vortex core rotates in the direction opposite to the runner rotation. The axial velocity profiles are observed to change from jet-like to wake-like during the formation of a vortex core. The large velocity gradients represent the sharp transition in the flow around the center axis of the draft tube. The severe pressure fluctuations corresponding to rotor–stator interaction and pressure waves are observed in the draft tube and vaneless space.

Categories: Latest papers in fluid mechanics

### Lattice Boltzmann simulations of droplet dynamics in two-phase separation with temperature field

Physics of Fluids, Volume 32, Issue 7, July 2020.

This paper adds a temperature field based on the Shan–Chen model and constructs a new model. The two-phase separation, fluid flow, and heat transfer characteristics under the temperature field were studied by using this model. The performance of the three processes of collision, interface opening, and coalescence experienced by droplet formation was analyzed in detail. The results show that the velocity and temperature on the liquid film of the droplet are symmetric with respect to the central position of the liquid film. Moreover, the droplet velocity is also symmetric about the center of the droplet, which provides a theoretical basis for the droplet to maintain stability. By changing the wall temperature difference, the temperature distribution formula in the square cavity is proposed, which is highly consistent with the simulated value, and the maximum error is 10.1%. The proposed new model makes a meaningful supplement to the improvement of two-phase separation.

This paper adds a temperature field based on the Shan–Chen model and constructs a new model. The two-phase separation, fluid flow, and heat transfer characteristics under the temperature field were studied by using this model. The performance of the three processes of collision, interface opening, and coalescence experienced by droplet formation was analyzed in detail. The results show that the velocity and temperature on the liquid film of the droplet are symmetric with respect to the central position of the liquid film. Moreover, the droplet velocity is also symmetric about the center of the droplet, which provides a theoretical basis for the droplet to maintain stability. By changing the wall temperature difference, the temperature distribution formula in the square cavity is proposed, which is highly consistent with the simulated value, and the maximum error is 10.1%. The proposed new model makes a meaningful supplement to the improvement of two-phase separation.

Categories: Latest papers in fluid mechanics

### Low-Mach hybrid lattice Boltzmann-finite difference solver for combustion in complex flows

Physics of Fluids, Volume 32, Issue 7, July 2020.

A hybrid solver for low-Mach combustion simulations has been proposed and validated through different test-cases in a previous publication [Hosseini et al., “Hybrid lattice Boltzmann-finite difference model for low Mach number combustion simulation,” Combust. Flame 209, 394–404 (2019)]. However, all the considered configurations were laminar, far from realistic applications. To check the performance of this approach for more complex physical processes, the developed solver is used here to model a variety of transitional and turbulent reacting flows. It is first used to compute an established benchmark, the Taylor–Green vortex, for (a) an iso-thermal single-component fluid, (b) a thermal non-reacting mixture, and (c) a thermal reacting mixture (hydrogen/air flame). Detailed comparisons of the results against a high-order in-house direct numerical simulation solver show that the proposed hybrid lattice Boltzmann solver correctly captures the dynamics of the flow at relatively low numerical cost. This same solver is then used to model the interaction of a methane/air flame with a vortex pair, revealing different interaction regimes of interest for turbulent combustion models. It is further employed to model the interaction of an expanding circular flame kernel with a pair of vortices and correctly captures the characteristic regimes. To showcase its ability to deal with turbulent flows, it is finally applied to a homogeneous isotropic turbulent configuration.

A hybrid solver for low-Mach combustion simulations has been proposed and validated through different test-cases in a previous publication [Hosseini et al., “Hybrid lattice Boltzmann-finite difference model for low Mach number combustion simulation,” Combust. Flame 209, 394–404 (2019)]. However, all the considered configurations were laminar, far from realistic applications. To check the performance of this approach for more complex physical processes, the developed solver is used here to model a variety of transitional and turbulent reacting flows. It is first used to compute an established benchmark, the Taylor–Green vortex, for (a) an iso-thermal single-component fluid, (b) a thermal non-reacting mixture, and (c) a thermal reacting mixture (hydrogen/air flame). Detailed comparisons of the results against a high-order in-house direct numerical simulation solver show that the proposed hybrid lattice Boltzmann solver correctly captures the dynamics of the flow at relatively low numerical cost. This same solver is then used to model the interaction of a methane/air flame with a vortex pair, revealing different interaction regimes of interest for turbulent combustion models. It is further employed to model the interaction of an expanding circular flame kernel with a pair of vortices and correctly captures the characteristic regimes. To showcase its ability to deal with turbulent flows, it is finally applied to a homogeneous isotropic turbulent configuration.

Categories: Latest papers in fluid mechanics

### Recurrence analysis and time extrapolation of a confined turbulent jet using modal decomposition

Physics of Fluids, Volume 32, Issue 7, July 2020.

We investigated the long-term dynamics of a turbulent, submerged jet at Re = 16 400 to develop a strategy for data-assisted, fast calculations of passive species transport. We obtained our data from high-fidelity large eddy simulations LES, which we validated against in-house particle image velocimetry measurements. The flow was split into coherent and incoherent fields using the method of proper orthogonal decomposition (POD). Depending on the number of POD modes to construct coherent velocity fields, different patterns in the recurrence plot of the system were found. For low mode numbers, line segments parallel to the main diagonal were present, which indicated that close states evolved similarly for a finite duration. Strong turbulent fluctuations in the original velocity fields, on the other hand, hid any large-scale recurrences and caused a structureless recurrence statistics. Using an iterated method of analogs, we time-extrapolated a short time series of coherent, distinctly recurring velocity fields of [math] to [math] and performed a study of species transport. We found that coherent dynamics alone could not reproduce LES results due to the lack of turbulent, small-scale fluctuations, but already a small set of incoherent flow fields sufficed to cure this shortcoming considerably. Surprisingly, time extrapolation of the original database without decomposition and without any obvious recurrences led to the best results in very close agreement with LES but with high demands regarding memory. Our data-assisted simulations outperformed LES on the same computational mesh by a speed-up factor of 15.

We investigated the long-term dynamics of a turbulent, submerged jet at Re = 16 400 to develop a strategy for data-assisted, fast calculations of passive species transport. We obtained our data from high-fidelity large eddy simulations LES, which we validated against in-house particle image velocimetry measurements. The flow was split into coherent and incoherent fields using the method of proper orthogonal decomposition (POD). Depending on the number of POD modes to construct coherent velocity fields, different patterns in the recurrence plot of the system were found. For low mode numbers, line segments parallel to the main diagonal were present, which indicated that close states evolved similarly for a finite duration. Strong turbulent fluctuations in the original velocity fields, on the other hand, hid any large-scale recurrences and caused a structureless recurrence statistics. Using an iterated method of analogs, we time-extrapolated a short time series of coherent, distinctly recurring velocity fields of [math] to [math] and performed a study of species transport. We found that coherent dynamics alone could not reproduce LES results due to the lack of turbulent, small-scale fluctuations, but already a small set of incoherent flow fields sufficed to cure this shortcoming considerably. Surprisingly, time extrapolation of the original database without decomposition and without any obvious recurrences led to the best results in very close agreement with LES but with high demands regarding memory. Our data-assisted simulations outperformed LES on the same computational mesh by a speed-up factor of 15.

Categories: Latest papers in fluid mechanics

### Unexpected rheological behavior of solutions of aromatic polyamide in transient physical states

Physics of Fluids, Volume 32, Issue 7, July 2020.

The subject of this study was an aromatic polyamide in dimethylacetamide/LiCl solutions in a concentration range from 0.5 vol. % – 5 vol. %. Dilute and semi-dilute solutions of this polymer demonstrate a complex of unexpected time- and temperature-dependent rheological effects under shearing in a heating–cooling cycle. In a static state, all systems under study are transparent solutions and no temperature-dependent thermal or visual effects are observed. However, superposition of shearing radically changes the situation. Heating up to 100 °C–140 °C leads to the phase separation with the coexistence of the amorphous and LC phases. On cooling of low-concentrated solutions, a decrease in the temperature leads to a several-times increase in the viscosity, and the subsequent viscosity decrease takes place at further temperature decrease. Both changes are kinetic effects. The first one is treated as an order-to-disorder transition. The decrease in viscosity is accompanied by a heat release, which reflects the reverse process of the disorder-to-order state transition. The isothermal viscosity decline in time is described by the Maxwell relaxation law with temperature-independent relaxation time. Hence, this is a non-temperature-activated process. At higher concentrations, strong temperature thixotropic behavior with much lower viscosity values on cooling, in comparison with the heating, is characteristic of these solutions due to their tendency for undercooling. The shear-induced transition, conjugated with the heat excess, was observed in semi-dilute solutions at the same temperature similar to that observed for dilute solutions. So during cooling under shearing, the solutions under study display a rather unusual phenomenon of a first-order transition. This type of phenomenon has not been described before. The phase transitions become quite evident in the polarized light. The observed kinetic effects in transient physical states are discussed on the basis of the concept of delayed and latent structure and phase transitions, including the formation of the LC state, which are initiated by the shearing.

The subject of this study was an aromatic polyamide in dimethylacetamide/LiCl solutions in a concentration range from 0.5 vol. % – 5 vol. %. Dilute and semi-dilute solutions of this polymer demonstrate a complex of unexpected time- and temperature-dependent rheological effects under shearing in a heating–cooling cycle. In a static state, all systems under study are transparent solutions and no temperature-dependent thermal or visual effects are observed. However, superposition of shearing radically changes the situation. Heating up to 100 °C–140 °C leads to the phase separation with the coexistence of the amorphous and LC phases. On cooling of low-concentrated solutions, a decrease in the temperature leads to a several-times increase in the viscosity, and the subsequent viscosity decrease takes place at further temperature decrease. Both changes are kinetic effects. The first one is treated as an order-to-disorder transition. The decrease in viscosity is accompanied by a heat release, which reflects the reverse process of the disorder-to-order state transition. The isothermal viscosity decline in time is described by the Maxwell relaxation law with temperature-independent relaxation time. Hence, this is a non-temperature-activated process. At higher concentrations, strong temperature thixotropic behavior with much lower viscosity values on cooling, in comparison with the heating, is characteristic of these solutions due to their tendency for undercooling. The shear-induced transition, conjugated with the heat excess, was observed in semi-dilute solutions at the same temperature similar to that observed for dilute solutions. So during cooling under shearing, the solutions under study display a rather unusual phenomenon of a first-order transition. This type of phenomenon has not been described before. The phase transitions become quite evident in the polarized light. The observed kinetic effects in transient physical states are discussed on the basis of the concept of delayed and latent structure and phase transitions, including the formation of the LC state, which are initiated by the shearing.

Categories: Latest papers in fluid mechanics

### The translational and rotational motions of a cylindrical particle in a granular shear flow inside a split bottom Couette cell

Physics of Fluids, Volume 32, Issue 7, July 2020.

The motion of a sample particle in a Couette-cell granular flow is measured using the magnetic particle tracking technology. This technology allows simultaneous measurements of translation and rotation of an individual grain in an opaque environment. The anisotropic sample particle is a cylinder with an aspect ratio 1, and the other grains in the flow are spherical balls. The trajectory shows that the particle in the studied Couette cell with a split bottom moves in a layered structure. The orientation distribution shows that the cylindrical particle prefers to align in specific directions, even though the aspect ratio is low and the shear motion should not cause strong alignment. A symbolic-based method is used to examine the jumping between spatial layers and the flipping among preferred directions. The result shows that the duration of particle staying in a preferred state is much longer than the duration of transition. In addition, a jumping particle has a higher chance to flip. In the bulk flow, the translational energy varies significantly along the radial direction. The magnitude of translational kinetic energy is generally much larger than the rotational motion.

The motion of a sample particle in a Couette-cell granular flow is measured using the magnetic particle tracking technology. This technology allows simultaneous measurements of translation and rotation of an individual grain in an opaque environment. The anisotropic sample particle is a cylinder with an aspect ratio 1, and the other grains in the flow are spherical balls. The trajectory shows that the particle in the studied Couette cell with a split bottom moves in a layered structure. The orientation distribution shows that the cylindrical particle prefers to align in specific directions, even though the aspect ratio is low and the shear motion should not cause strong alignment. A symbolic-based method is used to examine the jumping between spatial layers and the flipping among preferred directions. The result shows that the duration of particle staying in a preferred state is much longer than the duration of transition. In addition, a jumping particle has a higher chance to flip. In the bulk flow, the translational energy varies significantly along the radial direction. The magnitude of translational kinetic energy is generally much larger than the rotational motion.

Categories: Latest papers in fluid mechanics

### Transport coefficients of multi-component mixtures of noble gases based on ab initio potentials: Viscosity and thermal conductivity

Physics of Fluids, Volume 32, Issue 7, July 2020.

The viscosity and thermal conductivity of binary, ternary, and quaternary mixtures of helium, neon, argon, and krypton at low density are computed for wide ranges of temperatures and molar fractions, applying the Chapman–Enskog method. Ab initio interatomic potentials are employed in order to calculate the omega-integrals. The relative numerical errors of the viscosity and thermal conductivity do not exceed 10−6 and 10−5, respectively. The relative uncertainty related to the interatomic potential is about 0.1%. A comparison of the present data with results reported in other papers available in the literature shows a significant improvement of accuracy of the transport coefficients considered here.

The viscosity and thermal conductivity of binary, ternary, and quaternary mixtures of helium, neon, argon, and krypton at low density are computed for wide ranges of temperatures and molar fractions, applying the Chapman–Enskog method. Ab initio interatomic potentials are employed in order to calculate the omega-integrals. The relative numerical errors of the viscosity and thermal conductivity do not exceed 10−6 and 10−5, respectively. The relative uncertainty related to the interatomic potential is about 0.1%. A comparison of the present data with results reported in other papers available in the literature shows a significant improvement of accuracy of the transport coefficients considered here.

Categories: Latest papers in fluid mechanics

### Experimental investigation of turbulent wake flows in a helically wrapped rod bundle in presence of localized blockages

Physics of Fluids, Volume 32, Issue 7, July 2020.

In nuclear sodium fast reactors, bundles of rods are tightly packed into a triangular lattice, enclosed in a hexagonal duct, and each pin is spirally wrapped with a thin wire. Flow blockages can potentially impact the local flow characteristics and heat transfer mechanisms in the bundle due to its small subchannel size. The effects of the blockage on the flow structures and heat transfer mechanisms are important aspects that require an accurate investigation. In this study, the flow-field characteristics in the vicinity of a blockage located in the exterior subchannel of rod bundles with helically wrapped wires were experimentally investigated. The velocity fields in the exterior subchannel were acquired by applying matched-index-of-refraction and time-resolved particle image velocimetry (TR-PIV) techniques for Reynolds numbers of Re1 = 4000 and Re2 = 17 000, i.e., equivalent to Rew1 = 19 600 and Rew2 = 83 200, respectively, based on the blockage width. The results from the TR-PIV measurements revealed an arch-shaped vortex with a large flow recirculation and a pair of counter-rotating vortices in the wake region downstream of the blockage, which is commonly observed in the wake flow of bluff bodies. The relative lateral distance and angle between the two vortices decreased when the Reynolds numbers increased. Profiles of maximum turbulence intensity along the shear layers illustrated the transition process including the growth, peak, and decay along the flow direction. From the spectral analysis of the turbulent velocities extracted at points along the shear layer, the Strouhal numbers (St) representing the vortex shedding frequency were found to be St = 0.25 and St = 0.56 for the left and right shear layers, respectively. Characteristics of shear layers generated by the blockage in the exterior subchannel were investigated via the two-point cross correlation of fluctuating velocities. The spatiotemporal cross correlations of turbulent velocities, computed at points in the region where the left shear layer exhibited rolling effects and vortex breakdowns, were considerably wider and longer. The convection velocity Uc was estimated to be ∼0.82Um to 0.93Um. Proper orthogonal decomposition (POD) analysis was applied to the instantaneous velocity fields to extract the statistically dominant flow structures. It was found that POD modes 2–3 and 4–5 formed the pair modes when the corresponding POD temporal coefficients depicted sinusoidal shapes and exhibited nearly circular orbits in the phase space. Spectral analysis of the POD temporal coefficients confirmed the vortex shedding frequencies detected in the analysis of turbulent velocities.

In nuclear sodium fast reactors, bundles of rods are tightly packed into a triangular lattice, enclosed in a hexagonal duct, and each pin is spirally wrapped with a thin wire. Flow blockages can potentially impact the local flow characteristics and heat transfer mechanisms in the bundle due to its small subchannel size. The effects of the blockage on the flow structures and heat transfer mechanisms are important aspects that require an accurate investigation. In this study, the flow-field characteristics in the vicinity of a blockage located in the exterior subchannel of rod bundles with helically wrapped wires were experimentally investigated. The velocity fields in the exterior subchannel were acquired by applying matched-index-of-refraction and time-resolved particle image velocimetry (TR-PIV) techniques for Reynolds numbers of Re1 = 4000 and Re2 = 17 000, i.e., equivalent to Rew1 = 19 600 and Rew2 = 83 200, respectively, based on the blockage width. The results from the TR-PIV measurements revealed an arch-shaped vortex with a large flow recirculation and a pair of counter-rotating vortices in the wake region downstream of the blockage, which is commonly observed in the wake flow of bluff bodies. The relative lateral distance and angle between the two vortices decreased when the Reynolds numbers increased. Profiles of maximum turbulence intensity along the shear layers illustrated the transition process including the growth, peak, and decay along the flow direction. From the spectral analysis of the turbulent velocities extracted at points along the shear layer, the Strouhal numbers (St) representing the vortex shedding frequency were found to be St = 0.25 and St = 0.56 for the left and right shear layers, respectively. Characteristics of shear layers generated by the blockage in the exterior subchannel were investigated via the two-point cross correlation of fluctuating velocities. The spatiotemporal cross correlations of turbulent velocities, computed at points in the region where the left shear layer exhibited rolling effects and vortex breakdowns, were considerably wider and longer. The convection velocity Uc was estimated to be ∼0.82Um to 0.93Um. Proper orthogonal decomposition (POD) analysis was applied to the instantaneous velocity fields to extract the statistically dominant flow structures. It was found that POD modes 2–3 and 4–5 formed the pair modes when the corresponding POD temporal coefficients depicted sinusoidal shapes and exhibited nearly circular orbits in the phase space. Spectral analysis of the POD temporal coefficients confirmed the vortex shedding frequencies detected in the analysis of turbulent velocities.

Categories: Latest papers in fluid mechanics

### Aerodynamic instability of an inflatable aeroshell in suborbital re-entry

Physics of Fluids, Volume 32, Issue 7, July 2020.

Aerodynamic instability in the attitude of an inflatable re-entry vehicle in the subsonic regime has been observed during suborbital re-entry. This causes significant problems for aerodynamic decelerators using an inflatable aeroshell; thus, mitigating this problem is necessary. In this study, we revealed the instability mechanism using a computational science approach. To reproduce the in-flight oscillation motion in an unsteady turbulent flow field, we adopted a large-eddy simulation approach with a forced-oscillation technique. Computations were performed for two representative cases at transonic and subsonic speeds that were in stable and unstable states, respectively. Pitching moment hysteresis at a cycle in the motion was confirmed for the subsonic case, whereas such hysteresis did not appear for the transonic case. Pressures on the front surface and in the wake of the vehicle were obtained by employing a probe technique in the computations. Pressure phase delays at the surface and in the wake were confirmed as the pitch angle of the vehicle increased (pitch up) and decreased (pitch down), respectively. In particular, we observed that the wake structure formed by a large recirculation behavior significantly affected the pressure phase delay at the rear of the vehicle. The dynamic instability at subsonic speed resulted from flows that could not promptly follow the vehicle motion. Finally, the damping coefficients were evaluated for the design and development of the inflatable vehicle.

Aerodynamic instability in the attitude of an inflatable re-entry vehicle in the subsonic regime has been observed during suborbital re-entry. This causes significant problems for aerodynamic decelerators using an inflatable aeroshell; thus, mitigating this problem is necessary. In this study, we revealed the instability mechanism using a computational science approach. To reproduce the in-flight oscillation motion in an unsteady turbulent flow field, we adopted a large-eddy simulation approach with a forced-oscillation technique. Computations were performed for two representative cases at transonic and subsonic speeds that were in stable and unstable states, respectively. Pitching moment hysteresis at a cycle in the motion was confirmed for the subsonic case, whereas such hysteresis did not appear for the transonic case. Pressures on the front surface and in the wake of the vehicle were obtained by employing a probe technique in the computations. Pressure phase delays at the surface and in the wake were confirmed as the pitch angle of the vehicle increased (pitch up) and decreased (pitch down), respectively. In particular, we observed that the wake structure formed by a large recirculation behavior significantly affected the pressure phase delay at the rear of the vehicle. The dynamic instability at subsonic speed resulted from flows that could not promptly follow the vehicle motion. Finally, the damping coefficients were evaluated for the design and development of the inflatable vehicle.

Categories: Latest papers in fluid mechanics

### Experimental analysis of flashing front propagation in superheated water—Effects of degree of superheat, tube inclination, and secondary nucleation

Physics of Fluids, Volume 32, Issue 7, July 2020.

A comprehensive experimental investigation on free surface flashing and flashing front (FF) propagation after sudden depressurization of stagnant water is reported. Elaborate high-speed imaging and some limited pressure and temperature recording have been made using two experimental facilities. A new rupture mechanism has been developed, which offers a simple operation where the amount of depressurization can be controlled easily and precisely. For the first time, we have quantified the decrease in delay time with the degree of superheat. Facilities have been designed meticulously to cover a reasonable range of operating parameters and to eliminate spurious nucleations. We recorded the evolution and propagation of the free surface FF over the entire length of the test section (500 mm) and observed the propagation to be linear with a strong dependence on the degree of superheat. For the first time, we also reported the effect of secondary nucleation on the FF with elaborate imaging. Finally, we report our observation of FF dynamics in tubes for the entire range of inclinations for which to date no information is available. Our study reveals many unexplored aspects regarding flashing and more crucially pinpoints some important directions in which meticulous experiments are to be conducted in the future to understand this complex phenomenon better.

A comprehensive experimental investigation on free surface flashing and flashing front (FF) propagation after sudden depressurization of stagnant water is reported. Elaborate high-speed imaging and some limited pressure and temperature recording have been made using two experimental facilities. A new rupture mechanism has been developed, which offers a simple operation where the amount of depressurization can be controlled easily and precisely. For the first time, we have quantified the decrease in delay time with the degree of superheat. Facilities have been designed meticulously to cover a reasonable range of operating parameters and to eliminate spurious nucleations. We recorded the evolution and propagation of the free surface FF over the entire length of the test section (500 mm) and observed the propagation to be linear with a strong dependence on the degree of superheat. For the first time, we also reported the effect of secondary nucleation on the FF with elaborate imaging. Finally, we report our observation of FF dynamics in tubes for the entire range of inclinations for which to date no information is available. Our study reveals many unexplored aspects regarding flashing and more crucially pinpoints some important directions in which meticulous experiments are to be conducted in the future to understand this complex phenomenon better.

Categories: Latest papers in fluid mechanics

### Screech characteristics of under-expanded high aspect ratio elliptic jet

Physics of Fluids, Volume 32, Issue 7, July 2020.

Screeching behavior and the closure mechanism of a feedback loop for the flapping mode in under-expanded supersonic jet are investigated by schlieren imaging and near-field acoustic measurements for a high aspect ratio elliptic nozzle. Near-field measurements revealed a single screech frequency for the measured Mach number range. The cross spectrum of pressure signals shows that the upstream propagating wave is out of phase, which was identified as the asymmetric flapping mode. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods were applied to the time-resolved schlieren data to extract the coherent information associated with screech and its harmonics. The first three spatial POD modes reveal the periodic flapping of the jet and the asymmetric upstream propagation of acoustic waves. POD modes 4 and 5 identify the flow structures and acoustic wave patterns associated with the harmonics of the fundamental screech tone. The spatial DMD mode corresponds to the frequency of ∼10 kHz and exhibits the radial distortion of the jet shear layer and the acoustic radiation pattern. The interaction of the acoustic waves with the jet shear layer indicates that the upstream-traveling guided jet mode is responsible for closing the feedback loop of the flapping mode.

Screeching behavior and the closure mechanism of a feedback loop for the flapping mode in under-expanded supersonic jet are investigated by schlieren imaging and near-field acoustic measurements for a high aspect ratio elliptic nozzle. Near-field measurements revealed a single screech frequency for the measured Mach number range. The cross spectrum of pressure signals shows that the upstream propagating wave is out of phase, which was identified as the asymmetric flapping mode. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods were applied to the time-resolved schlieren data to extract the coherent information associated with screech and its harmonics. The first three spatial POD modes reveal the periodic flapping of the jet and the asymmetric upstream propagation of acoustic waves. POD modes 4 and 5 identify the flow structures and acoustic wave patterns associated with the harmonics of the fundamental screech tone. The spatial DMD mode corresponds to the frequency of ∼10 kHz and exhibits the radial distortion of the jet shear layer and the acoustic radiation pattern. The interaction of the acoustic waves with the jet shear layer indicates that the upstream-traveling guided jet mode is responsible for closing the feedback loop of the flapping mode.

Categories: Latest papers in fluid mechanics

### Effects of a triangular guide rib on flow and heat transfer in a turbulent jet impingement on an asymmetric concave surface

Physics of Fluids, Volume 32, Issue 7, July 2020.

In this study, a triangular guide rib (TGR) is designed with the aim of enhancing the heat transfer rate by accelerating a jet impinging downward on an asymmetric concave surface with curvature radii of 8 cm (Cr = 0.15) and 12 cm (Cr = 0.1). An infrared thermometer camera is employed to measure the temperature distribution in the steady-state condition. Predicted Nusselt number profiles by the renormalization group k–ε turbulent model go well with the experimental data. An equilateral triangular rib with each side measuring 12 mm (D/2) is placed in the stagnation region to investigate the effects of the TGR on flow and heat transfer of the asymmetric concave surface. This investigation is carried out for three different Reynolds numbers: 23 000, 35 000, and 50 000. The acceleration of the impinging jet due to the TGR creates a horseshoe-shape in the zone of high Nusselt number values. Numerical results show that the TGR provides higher averaged Nusselt numbers compared to a smooth concave surface.

In this study, a triangular guide rib (TGR) is designed with the aim of enhancing the heat transfer rate by accelerating a jet impinging downward on an asymmetric concave surface with curvature radii of 8 cm (Cr = 0.15) and 12 cm (Cr = 0.1). An infrared thermometer camera is employed to measure the temperature distribution in the steady-state condition. Predicted Nusselt number profiles by the renormalization group k–ε turbulent model go well with the experimental data. An equilateral triangular rib with each side measuring 12 mm (D/2) is placed in the stagnation region to investigate the effects of the TGR on flow and heat transfer of the asymmetric concave surface. This investigation is carried out for three different Reynolds numbers: 23 000, 35 000, and 50 000. The acceleration of the impinging jet due to the TGR creates a horseshoe-shape in the zone of high Nusselt number values. Numerical results show that the TGR provides higher averaged Nusselt numbers compared to a smooth concave surface.

Categories: Latest papers in fluid mechanics

### Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

Physics of Fluids, Volume 32, Issue 7, July 2020.

Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor–corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of the nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long short-term memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data, and the trained model can be retrained effectively due to the power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using the Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging artificial intelligence friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches.

Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor–corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of the nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long short-term memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data, and the trained model can be retrained effectively due to the power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using the Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging artificial intelligence friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches.

Categories: Latest papers in fluid mechanics

### Evolution and modulational instability of interfacial waves in a two-layer fluid with arbitrary layer depths

Physics of Fluids, Volume 32, Issue 7, July 2020.

A nonlinear Schrödinger equation (NLSE) describing the evolution of interfacial waves in a gravitationally stable, inviscid, incompressible, and irrotational two-layer fluid with arbitrary constant layer depths is derived using the multiple scale analysis method. The modulational instability (MI) of the interfacial waves is then analyzed using this NLSE. It is shown that the unstable region shrinks as the density ratio of the two layers increases and as each layer gets thinner. A requirement for unstable waves is that both the upper and lower layers are thicker than the critical depths for those layers. The critical depth of each layer as a function of the density ratio of two layers is obtained by curve fitting and used as a criterion for MI. Moreover, nine cases with various upper- and lower-layer depths are investigated. The relationships of the dark soliton to modulational stability and the bright soliton to MI are discussed in each case. In the unstable regions of the nine cases, it is found that the steepness of the perturbed interface amplitude increases, and the perturbed interface elevation decays more rapidly as the depth of each layer increases. Both the height and the steepness of the perturbed interface elevation increase with increasing density ratio of the two layers.

A nonlinear Schrödinger equation (NLSE) describing the evolution of interfacial waves in a gravitationally stable, inviscid, incompressible, and irrotational two-layer fluid with arbitrary constant layer depths is derived using the multiple scale analysis method. The modulational instability (MI) of the interfacial waves is then analyzed using this NLSE. It is shown that the unstable region shrinks as the density ratio of the two layers increases and as each layer gets thinner. A requirement for unstable waves is that both the upper and lower layers are thicker than the critical depths for those layers. The critical depth of each layer as a function of the density ratio of two layers is obtained by curve fitting and used as a criterion for MI. Moreover, nine cases with various upper- and lower-layer depths are investigated. The relationships of the dark soliton to modulational stability and the bright soliton to MI are discussed in each case. In the unstable regions of the nine cases, it is found that the steepness of the perturbed interface amplitude increases, and the perturbed interface elevation decays more rapidly as the depth of each layer increases. Both the height and the steepness of the perturbed interface elevation increase with increasing density ratio of the two layers.

Categories: Latest papers in fluid mechanics

### Entry pressure correlations in capillary flow

Physics of Fluids, Volume 32, Issue 7, July 2020.

The entry pressure in capillary rheometry is determined by using the Bagley correction method to accurately determine the viscosity of polymers at high shear rates. This method requires the use of at least three capillary dies having the same diameter and different lengths. In this paper, the entry pressure of over 40 sets of experimental data for different polymers is correlated as a function of wall shear stress for two different classes of polymers, namely, linear and branched. The derived correlations can directly be applied to correct the raw capillary data from a single capillary die, thus minimizing the experimental error, effort, and time.

The entry pressure in capillary rheometry is determined by using the Bagley correction method to accurately determine the viscosity of polymers at high shear rates. This method requires the use of at least three capillary dies having the same diameter and different lengths. In this paper, the entry pressure of over 40 sets of experimental data for different polymers is correlated as a function of wall shear stress for two different classes of polymers, namely, linear and branched. The derived correlations can directly be applied to correct the raw capillary data from a single capillary die, thus minimizing the experimental error, effort, and time.

Categories: Latest papers in fluid mechanics