# Latest papers in fluid mechanics

### Profile of a two-dimensional vortex condensate beyond the universal limit

Author(s): Vladimir Parfenyev

It is well known that an inverse turbulent cascade in a finite (2π×2π) two-dimensional periodic domain leads to the emergence of a system-sized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly…

[Phys. Rev. E 106, 025102] Published Wed Aug 10, 2022

Categories: Latest papers in fluid mechanics

### Space-streamline-based method of characteristics for inverse design of three-dimensional super/hypersonic flows

Physics of Fluids, Volume 34, Issue 8, August 2022.

The inverse design of super/hypersonic flows is widely utilized in aerospace, especially in waveriders, inlets, and nozzles. However, most of the existing methods are intended for the two-dimensional (2D) problem. The inverse method for generalized three-dimensional (3D) supersonic flows is still immature and is the main purpose of the space-streamline-based method of characteristics (SMOC) presented in this paper. The key of SMOC is to integrate an additional Euler predictor–corrector algorithm for pressure gradients in the unit calculation process. In this way, the temporary orientation of the osculating plane (OP) of the space streamline is determined, and the conventional 2D axisymmetric method of characteristics can be adopted in the OP. Three common unit processes of SMOC and the posedness are introduced, and the astringency is demonstrated by corresponding algebraic calculations. With this method, inviscid super/hypersonic flows can be solved on the basis of specified flow features, such as a 3D shock surface or a 3D wall pressure distribution. The accuracy and efficiency of SMOC are verified by using an inverse design example, that is, the flow produced by an elliptic conical surface at a freestream Mach number of 6. The numerical simulation of the inverse design result indicates that the 3D shock wave geometry and the 3D wall pressure distribution match the targets completely. The relative root-mean-squared error of the surface geometry is 10−3 magnitude, and the computation time cost of the inverse design is less than that of the general direct Euler solver.

The inverse design of super/hypersonic flows is widely utilized in aerospace, especially in waveriders, inlets, and nozzles. However, most of the existing methods are intended for the two-dimensional (2D) problem. The inverse method for generalized three-dimensional (3D) supersonic flows is still immature and is the main purpose of the space-streamline-based method of characteristics (SMOC) presented in this paper. The key of SMOC is to integrate an additional Euler predictor–corrector algorithm for pressure gradients in the unit calculation process. In this way, the temporary orientation of the osculating plane (OP) of the space streamline is determined, and the conventional 2D axisymmetric method of characteristics can be adopted in the OP. Three common unit processes of SMOC and the posedness are introduced, and the astringency is demonstrated by corresponding algebraic calculations. With this method, inviscid super/hypersonic flows can be solved on the basis of specified flow features, such as a 3D shock surface or a 3D wall pressure distribution. The accuracy and efficiency of SMOC are verified by using an inverse design example, that is, the flow produced by an elliptic conical surface at a freestream Mach number of 6. The numerical simulation of the inverse design result indicates that the 3D shock wave geometry and the 3D wall pressure distribution match the targets completely. The relative root-mean-squared error of the surface geometry is 10−3 magnitude, and the computation time cost of the inverse design is less than that of the general direct Euler solver.

Categories: Latest papers in fluid mechanics

### Propeller wake instabilities under turbulent-inflow conditions

Physics of Fluids, Volume 34, Issue 8, August 2022.

The wake instabilities of a propeller operating under turbulent-inflow conditions were studied by the improved delayed detached eddy simulation method on an unstructured mesh consisting of almost 82.5 × 106 cells, capturing propeller wakes extending to the downstream distance of 9D (where D is the propeller diameter). Two turbulent-inflow cases with the turbulence intensity of 5% and 20% were considered. The mean loads and phase-averaged flow field show good agreement with experiments. As the propeller blade interacts with the turbulent inflow, a wide peak extending approximately ±10 Hz in the power spectral density of the time histories of the thrust and torque coefficient. Simulation results reveal wake instability mechanisms of the propeller operating under different turbulent-inflow conditions. The turbulence added to the inlet boundary interacts with the tip vortices, which accelerates the destabilization processes of the tip vortex system from two aspects. First, the interaction between the inflow turbulence and the tip vortex promotes the diffusion of tip vortices. Second, the interaction between the inflow turbulence and the tip vortices magnifies the instability motion of the tip vortex. The wake vortex system of the high-turbulence inflow condition loses its stability after 2.2D downstream, while the initial instability behaviors for the low-turbulence inflow condition are observed at the location of 3.4D downstream. The present study presents a deeper insight into the flow physics driving the tip vortex pairing process for a propeller operating under turbulent-inflow conditions.

The wake instabilities of a propeller operating under turbulent-inflow conditions were studied by the improved delayed detached eddy simulation method on an unstructured mesh consisting of almost 82.5 × 106 cells, capturing propeller wakes extending to the downstream distance of 9D (where D is the propeller diameter). Two turbulent-inflow cases with the turbulence intensity of 5% and 20% were considered. The mean loads and phase-averaged flow field show good agreement with experiments. As the propeller blade interacts with the turbulent inflow, a wide peak extending approximately ±10 Hz in the power spectral density of the time histories of the thrust and torque coefficient. Simulation results reveal wake instability mechanisms of the propeller operating under different turbulent-inflow conditions. The turbulence added to the inlet boundary interacts with the tip vortices, which accelerates the destabilization processes of the tip vortex system from two aspects. First, the interaction between the inflow turbulence and the tip vortex promotes the diffusion of tip vortices. Second, the interaction between the inflow turbulence and the tip vortices magnifies the instability motion of the tip vortex. The wake vortex system of the high-turbulence inflow condition loses its stability after 2.2D downstream, while the initial instability behaviors for the low-turbulence inflow condition are observed at the location of 3.4D downstream. The present study presents a deeper insight into the flow physics driving the tip vortex pairing process for a propeller operating under turbulent-inflow conditions.

Categories: Latest papers in fluid mechanics

### Experimental investigation on the effect of fluid–structure interaction on unsteady cavitating flows around flexible and stiff hydrofoils

Physics of Fluids, Volume 34, Issue 8, August 2022.

We experimentally investigated the effect of fluid–structure interaction on unsteady cavitating flows around flexible and stiff National Advisory Committee for Aeronautics 0015 hydrofoils in a low-pressure cavitation tunnel. We analyzed the cavitating dynamics by capturing the cavitation dynamics using two high-speed cameras at different cavitating regimes on the surface of the hydrofoils, made of polyvinyl chloride, brass, and aluminum. We then measured the associated structural deformations in specific cavitation regime such as cloud and partial cavitation dynamics, using a digital image correlation technique. The hydrofoil's angle of attack was set to 10°, and the flow's Reynolds number was adjusted to 0.6 × 106. Results showed that the cavity's shedding frequency on the flexible hydrofoil shifted faster to a higher frequency than on the stiff hydrofoils under similar cavitating conditions. The flexible hydrofoil underwent strong structural oscillations at the low cavitation number for the cloud cavitation regime. The associated amplitudes of the vibration were about 20 times higher than those of the hydrofoil made of brass. It was observed that the fluid–structure interaction can significantly affect the cavitation-induced vibration of the flexible hydrofoil.

We experimentally investigated the effect of fluid–structure interaction on unsteady cavitating flows around flexible and stiff National Advisory Committee for Aeronautics 0015 hydrofoils in a low-pressure cavitation tunnel. We analyzed the cavitating dynamics by capturing the cavitation dynamics using two high-speed cameras at different cavitating regimes on the surface of the hydrofoils, made of polyvinyl chloride, brass, and aluminum. We then measured the associated structural deformations in specific cavitation regime such as cloud and partial cavitation dynamics, using a digital image correlation technique. The hydrofoil's angle of attack was set to 10°, and the flow's Reynolds number was adjusted to 0.6 × 106. Results showed that the cavity's shedding frequency on the flexible hydrofoil shifted faster to a higher frequency than on the stiff hydrofoils under similar cavitating conditions. The flexible hydrofoil underwent strong structural oscillations at the low cavitation number for the cloud cavitation regime. The associated amplitudes of the vibration were about 20 times higher than those of the hydrofoil made of brass. It was observed that the fluid–structure interaction can significantly affect the cavitation-induced vibration of the flexible hydrofoil.

Categories: Latest papers in fluid mechanics

### Prediction of broadband noise from rotating blade elements with serrated trailing edges

Physics of Fluids, Volume 34, Issue 8, August 2022.

This paper conducts a theoretical investigation into the prediction of broadband trailing-edge noise for rotating serrated blades. Lyu's semi-analytical noise prediction model for isolated flat plates is extended to rotating blades using Schlinker and Amiet's approach and applied to three test applications including a wind turbine, a cooling fan, and an open propeller. The model is validated by comparing the straight edge results with that presented in the work of Sinayoko et al., which shows an excellent agreement. The noise spectra obtained using different-order approximations show that the second-order solution yields a converged result. It is found that trailing-edge serrations can lead to noise reduction in the intermediate- and high-frequency ranges at an observer angle of 45° at low Mach numbers but may lead to noise increase in the intermediate-frequency range at high Mach numbers. The results show that the directivity patterns change due to the use of trailing-edge serrations and the directivity peaks are observed at high frequencies. A detailed analysis on the effects of rotation shows that for low-Mach number applications, the Doppler effect is weak and the peaky directivity pattern is mainly affected by the nonuniform directivity of an isolated flat plate at high frequencies. However, for high-Mach number applications, the Doppler effect is significant and also contributes to the final directivity pattern of rotating blades.

This paper conducts a theoretical investigation into the prediction of broadband trailing-edge noise for rotating serrated blades. Lyu's semi-analytical noise prediction model for isolated flat plates is extended to rotating blades using Schlinker and Amiet's approach and applied to three test applications including a wind turbine, a cooling fan, and an open propeller. The model is validated by comparing the straight edge results with that presented in the work of Sinayoko et al., which shows an excellent agreement. The noise spectra obtained using different-order approximations show that the second-order solution yields a converged result. It is found that trailing-edge serrations can lead to noise reduction in the intermediate- and high-frequency ranges at an observer angle of 45° at low Mach numbers but may lead to noise increase in the intermediate-frequency range at high Mach numbers. The results show that the directivity patterns change due to the use of trailing-edge serrations and the directivity peaks are observed at high frequencies. A detailed analysis on the effects of rotation shows that for low-Mach number applications, the Doppler effect is weak and the peaky directivity pattern is mainly affected by the nonuniform directivity of an isolated flat plate at high frequencies. However, for high-Mach number applications, the Doppler effect is significant and also contributes to the final directivity pattern of rotating blades.

Categories: Latest papers in fluid mechanics

### Turbulent channel flow controlled by traveling-wave-like body force mimicking oscillating thin films

Physics of Fluids, Volume 34, Issue 8, August 2022.

To improve energy efficiency, flow control techniques for skin-friction drag and heat transfer with regard to wall turbulence are essential. This study performs direct numerical simulation of turbulent channel flows. The traveling-wave-like body force is employed as the flow control technique to break the similarity between momentum and heat transfer. The traveling wave control mimics the self-excited thin film in the corresponding experimental study. When the wave traveled slowly along the downstream direction, the skin-friction drag, heat transfer, and analogy factor were found to increase. Moreover, these parameters increased with an increase in the reference height of the traveling wave (hw). Flow visualization shows turbulence enhancement owing to the increase in hw. Three-component decomposition elucidates the difference between the control effect on the Reynolds shear stress and the turbulent heat flux.

To improve energy efficiency, flow control techniques for skin-friction drag and heat transfer with regard to wall turbulence are essential. This study performs direct numerical simulation of turbulent channel flows. The traveling-wave-like body force is employed as the flow control technique to break the similarity between momentum and heat transfer. The traveling wave control mimics the self-excited thin film in the corresponding experimental study. When the wave traveled slowly along the downstream direction, the skin-friction drag, heat transfer, and analogy factor were found to increase. Moreover, these parameters increased with an increase in the reference height of the traveling wave (hw). Flow visualization shows turbulence enhancement owing to the increase in hw. Three-component decomposition elucidates the difference between the control effect on the Reynolds shear stress and the turbulent heat flux.

Categories: Latest papers in fluid mechanics

### Implications of dragonfly's muscle control on flapping kinematics and aerodynamics

Physics of Fluids, Volume 34, Issue 8, August 2022.

In this work, we designed and characterized a passive structural wing actuation setup that was able to realistically mimic the flapping and pitching kinematics of dragonflies. In this setup, an inelastic string limited the wing pitch that may be sufficiently simple for practical micro air vehicle applications. To further evaluate the dominance of inertial passive and active muscle-controlled pitch actuation in dragonfly flight, the flow fields and pitching angle variations of the naturally actuated wing of a tethered dragonfly were compared with that of the same wing artificially actuated via a proposed passive mechanism. We found that passive rotation characterizes most of the forewing flapping cycle except the upstroke reversal where the dragonfly uses its muscle movement to accelerate its forewing rotation. The measured flow fields show that accelerated wing rotation at the upstroke reversal will result in a stronger leading edge vortex during the downstroke, the additional force from which is estimated to account for 4.3% of the total cycle averaged force generated.

In this work, we designed and characterized a passive structural wing actuation setup that was able to realistically mimic the flapping and pitching kinematics of dragonflies. In this setup, an inelastic string limited the wing pitch that may be sufficiently simple for practical micro air vehicle applications. To further evaluate the dominance of inertial passive and active muscle-controlled pitch actuation in dragonfly flight, the flow fields and pitching angle variations of the naturally actuated wing of a tethered dragonfly were compared with that of the same wing artificially actuated via a proposed passive mechanism. We found that passive rotation characterizes most of the forewing flapping cycle except the upstroke reversal where the dragonfly uses its muscle movement to accelerate its forewing rotation. The measured flow fields show that accelerated wing rotation at the upstroke reversal will result in a stronger leading edge vortex during the downstroke, the additional force from which is estimated to account for 4.3% of the total cycle averaged force generated.

Categories: Latest papers in fluid mechanics

### Numerical investigation of an insect-scale flexible wing with a small amplitude flapping kinematics

Physics of Fluids, Volume 34, Issue 8, August 2022.

To maintain flight, insect-scale air vehicles must adapt to their low Reynolds number flight conditions and generate sufficient aerodynamic force. Researchers conducted extensive studies to explore the mechanism of high aerodynamic efficiency on such a small scale. In this paper, a centimeter-level flapping wing is used to investigate the mechanism and feasibility of whether a simple motion with a certain frequency can generate enough lift. The unsteady numerical simulations are based on the fluid structure interaction (FSI) method and dynamic mesh technology. The flapping motion is in a simple harmonic law of small amplitude with high frequency, which corresponds to the flapping wing driven by a piezoelectric actuator. The inertial and aerodynamic forces of the wing can cause chordwise torsion, thereby generating the vertical aerodynamic force. The concerned flapping frequency refers to the structural modal frequency and FSI modal frequency. According to the results, we find that under the condition that frequency ratio is 1.0, that is, when the wing flaps at the first-order structural modal frequency, the deformation degree of the wing is the highest, but it does not produce good aerodynamic performance. However, under the condition that frequency ratio is 0.822, when the wing flaps at the first-order FSI modal frequency, the aerodynamic efficiency achieve the highest and is equal to 0.273. Under the condition that frequency ratio is 0.6, that is, when the wing flaps at a frequency smaller than the first-order FSI modal frequency, the flapping wing effectively utilizes the strain energy storage and release mechanism and produces the maximum vertical coefficient which is equal to 4.86. The study shows that this flapping motion can satisfy the requirements of lift to sustain the flight on this scale.

To maintain flight, insect-scale air vehicles must adapt to their low Reynolds number flight conditions and generate sufficient aerodynamic force. Researchers conducted extensive studies to explore the mechanism of high aerodynamic efficiency on such a small scale. In this paper, a centimeter-level flapping wing is used to investigate the mechanism and feasibility of whether a simple motion with a certain frequency can generate enough lift. The unsteady numerical simulations are based on the fluid structure interaction (FSI) method and dynamic mesh technology. The flapping motion is in a simple harmonic law of small amplitude with high frequency, which corresponds to the flapping wing driven by a piezoelectric actuator. The inertial and aerodynamic forces of the wing can cause chordwise torsion, thereby generating the vertical aerodynamic force. The concerned flapping frequency refers to the structural modal frequency and FSI modal frequency. According to the results, we find that under the condition that frequency ratio is 1.0, that is, when the wing flaps at the first-order structural modal frequency, the deformation degree of the wing is the highest, but it does not produce good aerodynamic performance. However, under the condition that frequency ratio is 0.822, when the wing flaps at the first-order FSI modal frequency, the aerodynamic efficiency achieve the highest and is equal to 0.273. Under the condition that frequency ratio is 0.6, that is, when the wing flaps at a frequency smaller than the first-order FSI modal frequency, the flapping wing effectively utilizes the strain energy storage and release mechanism and produces the maximum vertical coefficient which is equal to 4.86. The study shows that this flapping motion can satisfy the requirements of lift to sustain the flight on this scale.

Categories: Latest papers in fluid mechanics

### Surface design of superhydrophobic parallel grooves for controllable petal bouncing and contact time reduction

Physics of Fluids, Volume 34, Issue 8, August 2022.

This study numerically investigates the bouncing characteristics of impacting droplets on superhydrophobic sub-millimeter parallel grooves by the level-set method. Once the Weber number (We) is increased to a critical value (Wec), a unique petal-like droplet bouncing off the parallel grooves without horizontal retraction is found, dramatically reducing the contact time (tc) by up to ∼75%. Such a bouncing mode is attributed to the rectification of capillary energy stored in the penetrated liquids into upward motion. To achieve controllable petal bouncing, the coupling effects of impact velocity and surface geometric characteristics on tc and Wec are elucidated from the perspective of timescale, momentum, and energy. The numerical results indicate that narrowing the center-to-center spacing contributes to shortening tc and slowing down the growth of tc with We. In contrast, the effect of ridge height is negligible. By establishing the model of emptying time, the relationships of tc with impact velocity and geometric parameters are quantitatively identified. Furthermore, along with the strengthened anisotropic property, a large center-to-center spacing promotes the conversion of horizontal momentum into vertical momentum and suppresses the increment of surface energy, thus inducing the reduction in Wec. Distinct from known anisotropic surfaces in the previous work, the anisotropic property of parallel-grooved surface plays an opposite role in shortening tc. Finally, incorporating the energy balance approach, a semi-empirical model is developed to predict Wec, exhibiting good agreement with present simulation. This work provides physical insights into petal bouncing and inspires the design of textured surfaces to reduce contact time.

This study numerically investigates the bouncing characteristics of impacting droplets on superhydrophobic sub-millimeter parallel grooves by the level-set method. Once the Weber number (We) is increased to a critical value (Wec), a unique petal-like droplet bouncing off the parallel grooves without horizontal retraction is found, dramatically reducing the contact time (tc) by up to ∼75%. Such a bouncing mode is attributed to the rectification of capillary energy stored in the penetrated liquids into upward motion. To achieve controllable petal bouncing, the coupling effects of impact velocity and surface geometric characteristics on tc and Wec are elucidated from the perspective of timescale, momentum, and energy. The numerical results indicate that narrowing the center-to-center spacing contributes to shortening tc and slowing down the growth of tc with We. In contrast, the effect of ridge height is negligible. By establishing the model of emptying time, the relationships of tc with impact velocity and geometric parameters are quantitatively identified. Furthermore, along with the strengthened anisotropic property, a large center-to-center spacing promotes the conversion of horizontal momentum into vertical momentum and suppresses the increment of surface energy, thus inducing the reduction in Wec. Distinct from known anisotropic surfaces in the previous work, the anisotropic property of parallel-grooved surface plays an opposite role in shortening tc. Finally, incorporating the energy balance approach, a semi-empirical model is developed to predict Wec, exhibiting good agreement with present simulation. This work provides physical insights into petal bouncing and inspires the design of textured surfaces to reduce contact time.

Categories: Latest papers in fluid mechanics

### Fragmentation of inviscid liquid and destination of satellite droplets

Physics of Fluids, Volume 34, Issue 8, August 2022.

The breakup process of the inviscid liquid bridge sandwiched between two coaxial and equal-sized rods is investigated by tracking its profile. Here, the focus is on the quasi-static profile of the liquid bridge close to rupture and its influence on the subsequent dynamic breakup behaviors. With the increasing distance between the two rods, the profile of the liquid bridge close to rupture undergoes a transition from symmetry to asymmetry. We found there exists a critical slenderness above which the liquid bridge will be asymmetric and present a profile that can be well fitted by one cycle of the sine wave. It is demonstrated both experimentally and theoretically that the ratio of the length of the bridge to its equivalent radius, defined as geometric mean of the radii at the peak and trough of the bridge, is always [math] for the asymmetric bridge close to rupture. Different with the symmetric evolution of the short bridge, the long asymmetric bridge pinches off first from the side near the bigger sessile drop and then from the other side, which endows the satellite droplet with a lateral momentum, resulting in the satellite re-collected by the sessile drop. The influence of the slenderness on the time interval among the asymmetric pinch-off, velocity, destination, and size of the satellite was investigated. A scaling law was proposed to describe the relationship between the lateral momentum of the satellite and the time interval between two pinch-off. This work is expected to benefit the utilizing or suppressing the satellite in practice.

The breakup process of the inviscid liquid bridge sandwiched between two coaxial and equal-sized rods is investigated by tracking its profile. Here, the focus is on the quasi-static profile of the liquid bridge close to rupture and its influence on the subsequent dynamic breakup behaviors. With the increasing distance between the two rods, the profile of the liquid bridge close to rupture undergoes a transition from symmetry to asymmetry. We found there exists a critical slenderness above which the liquid bridge will be asymmetric and present a profile that can be well fitted by one cycle of the sine wave. It is demonstrated both experimentally and theoretically that the ratio of the length of the bridge to its equivalent radius, defined as geometric mean of the radii at the peak and trough of the bridge, is always [math] for the asymmetric bridge close to rupture. Different with the symmetric evolution of the short bridge, the long asymmetric bridge pinches off first from the side near the bigger sessile drop and then from the other side, which endows the satellite droplet with a lateral momentum, resulting in the satellite re-collected by the sessile drop. The influence of the slenderness on the time interval among the asymmetric pinch-off, velocity, destination, and size of the satellite was investigated. A scaling law was proposed to describe the relationship between the lateral momentum of the satellite and the time interval between two pinch-off. This work is expected to benefit the utilizing or suppressing the satellite in practice.

Categories: Latest papers in fluid mechanics

### Water entry dynamics of rough microstructured spheres

Physics of Fluids, Volume 34, Issue 8, August 2022.

In this work, we proposed a facile underwater air cavity generation strategy based on rough microstructured spheres and explored its water entry dynamics and drag reduction characteristics. Under the assistance of microstructures, the three-phase contact line is pinned near the sphere equator and inhibits the wetting of the liquid film along the sphere surface, so that leading the formation of air cavity. The water entry process is mainly divided into four stages: flow formation, cavity opening and stretching, cavity closure and entrapment, and cavity collapse. With the Froude number Fr, the pinch-off depth of air cavity obviously increases, and the pinch-off time is also delayed, which contributes to the formation of a longer bottom air cavity. In addition, the spheres with a larger impact velocity would fall faster in water during the initial falling period, while the terminal velocities are nearly the same for all the spheres when they are in a stable falling period. It is worth noting that for a same sphere, the larger impact velocity could not only contribute to the formation of a longer air cavity but also makes the generated air cavity keep in a stable and streamlined shape at different underwater depth, which is vitally important for achieving continuous drag reduction. Finally, we demonstrated numerically that the stable streamlined sphere-in-cavity structure could reduce the hydrodynamic resistance levels up to 91.3% at Re ∼ 3.12 × 104, which is related to the boundary slip caused by an air layer trapped in the microstructures.

In this work, we proposed a facile underwater air cavity generation strategy based on rough microstructured spheres and explored its water entry dynamics and drag reduction characteristics. Under the assistance of microstructures, the three-phase contact line is pinned near the sphere equator and inhibits the wetting of the liquid film along the sphere surface, so that leading the formation of air cavity. The water entry process is mainly divided into four stages: flow formation, cavity opening and stretching, cavity closure and entrapment, and cavity collapse. With the Froude number Fr, the pinch-off depth of air cavity obviously increases, and the pinch-off time is also delayed, which contributes to the formation of a longer bottom air cavity. In addition, the spheres with a larger impact velocity would fall faster in water during the initial falling period, while the terminal velocities are nearly the same for all the spheres when they are in a stable falling period. It is worth noting that for a same sphere, the larger impact velocity could not only contribute to the formation of a longer air cavity but also makes the generated air cavity keep in a stable and streamlined shape at different underwater depth, which is vitally important for achieving continuous drag reduction. Finally, we demonstrated numerically that the stable streamlined sphere-in-cavity structure could reduce the hydrodynamic resistance levels up to 91.3% at Re ∼ 3.12 × 104, which is related to the boundary slip caused by an air layer trapped in the microstructures.

Categories: Latest papers in fluid mechanics

### Trajectory-optimized cluster-based network model for the sphere wake

Physics of Fluids, Volume 34, Issue 8, August 2022.

We propose a novel trajectory-optimized cluster-based network model (tCNM) for nonlinear model order reduction from time-resolved data following Li et al. [“Cluster-based network model,” J. Fluid Mech. 906, A21 (2021)] and improving the accuracy for a given number of centroids. The starting point is k-means++ clustering, which minimizes the representation error of the snapshots by their closest centroids. The dynamics is presented by “flights” between the centroids. The proposed trajectory-optimized clustering aims to reduce the kinematic representation error further by shifting the centroids closer to the snapshot trajectory and refining state propagation with trajectory support points. Thus, curved trajectories are better resolved. The resulting tCNM is demonstrated for the sphere wake for three flow regimes, including the periodic, quasi-periodic, and chaotic dynamics. The representation error of tCNM is five times smaller as compared to the approximation by the closest centroid. Thus, the error is at the same level as proper orthogonal decomposition (POD) of same order. Yet, tCNM has distinct advantages over POD modeling: it is human interpretable by representing dynamics by a handful of coherent structures and their transitions; it shows robust dynamics by design, i.e., stable long-time behavior; and its development is fully automatable, i.e., it does not require tunable auxiliary closure and other models.

We propose a novel trajectory-optimized cluster-based network model (tCNM) for nonlinear model order reduction from time-resolved data following Li et al. [“Cluster-based network model,” J. Fluid Mech. 906, A21 (2021)] and improving the accuracy for a given number of centroids. The starting point is k-means++ clustering, which minimizes the representation error of the snapshots by their closest centroids. The dynamics is presented by “flights” between the centroids. The proposed trajectory-optimized clustering aims to reduce the kinematic representation error further by shifting the centroids closer to the snapshot trajectory and refining state propagation with trajectory support points. Thus, curved trajectories are better resolved. The resulting tCNM is demonstrated for the sphere wake for three flow regimes, including the periodic, quasi-periodic, and chaotic dynamics. The representation error of tCNM is five times smaller as compared to the approximation by the closest centroid. Thus, the error is at the same level as proper orthogonal decomposition (POD) of same order. Yet, tCNM has distinct advantages over POD modeling: it is human interpretable by representing dynamics by a handful of coherent structures and their transitions; it shows robust dynamics by design, i.e., stable long-time behavior; and its development is fully automatable, i.e., it does not require tunable auxiliary closure and other models.

Categories: Latest papers in fluid mechanics

### Study on the mechanism of shock wave and boundary layer interaction control using high-frequency pulsed arc discharge plasma

Physics of Fluids, Volume 34, Issue 8, August 2022.

This paper studies the response characteristics of shock wave and boundary layer interaction (SWBLI) controlled by high-frequency pulsed arc discharge (PAD) in a Mach 2.5 flow. The dynamic evolution of SWBLI disturbed by arc plasma energy deposition was captured, and the controlling mechanism under different exciting power and frequency was explored. The results showed that the blast wave induced by PADs had a strong impact on SWBLI structures and distorted the separation shock wave. During the downstream propagation, the controlling gas bubbles (CGBs) delivered a continuous thermal excitation to the boundary layer and reached the maximum penetration depth near the semi-cylinder. The arc discharge in the SWBLI region induced larger energy deposition, which made the heating zone obtain the highest initial temperature and longest heating duration. Under the plasma condition of 1 × 1011 W/m3/15 kHz, both the upstream part of the shear layer and the foot portion of the reattachment shock wave were removed. When setting the excitation to 2.5 × 1010 W/m3/60 kHz, a thermal exciting surface of merged CGBs was formed and the separation shock wave was completely replaced by an equivalent compression-wave system. A better drag-reduction effect on the flow field would be produced by the actuator with an increased operating power or frequency, and a drag reduction rate of nearly 25.5% was achieved under the 2.5 × 1010 W/m3/60 kHz control condition.

This paper studies the response characteristics of shock wave and boundary layer interaction (SWBLI) controlled by high-frequency pulsed arc discharge (PAD) in a Mach 2.5 flow. The dynamic evolution of SWBLI disturbed by arc plasma energy deposition was captured, and the controlling mechanism under different exciting power and frequency was explored. The results showed that the blast wave induced by PADs had a strong impact on SWBLI structures and distorted the separation shock wave. During the downstream propagation, the controlling gas bubbles (CGBs) delivered a continuous thermal excitation to the boundary layer and reached the maximum penetration depth near the semi-cylinder. The arc discharge in the SWBLI region induced larger energy deposition, which made the heating zone obtain the highest initial temperature and longest heating duration. Under the plasma condition of 1 × 1011 W/m3/15 kHz, both the upstream part of the shear layer and the foot portion of the reattachment shock wave were removed. When setting the excitation to 2.5 × 1010 W/m3/60 kHz, a thermal exciting surface of merged CGBs was formed and the separation shock wave was completely replaced by an equivalent compression-wave system. A better drag-reduction effect on the flow field would be produced by the actuator with an increased operating power or frequency, and a drag reduction rate of nearly 25.5% was achieved under the 2.5 × 1010 W/m3/60 kHz control condition.

Categories: Latest papers in fluid mechanics

### High frequency Rayleigh scattering measurements of density fluctuations in high-pressure premixed combustion

Physics of Fluids, Volume 34, Issue 8, August 2022.

Measuring physical flow properties, such as density and temperature, at high frequency in high temperature and pressure environments is very challenging. Rapid fluctuations of these properties often have an impact on combustion efficiency and stability. We hereby attempt to measure density fluctuations in high-pressure premixed combustion using high temporal resolution laser Rayleigh scattering. The Rayleigh scattering intensity was assessed by counting individual photons due to the low signal to noise ratio. The measurement system was first verified at various air pressures without combustion. Combustion experiments were then conducted at four different pressures, from 1 to 7 bar. The density fluctuations increased with pressure, but the dominant fluctuation frequency decreased. Proper orthogonal decomposition analysis of high-speed schlieren images of the flame front was used to verify the results.

Measuring physical flow properties, such as density and temperature, at high frequency in high temperature and pressure environments is very challenging. Rapid fluctuations of these properties often have an impact on combustion efficiency and stability. We hereby attempt to measure density fluctuations in high-pressure premixed combustion using high temporal resolution laser Rayleigh scattering. The Rayleigh scattering intensity was assessed by counting individual photons due to the low signal to noise ratio. The measurement system was first verified at various air pressures without combustion. Combustion experiments were then conducted at four different pressures, from 1 to 7 bar. The density fluctuations increased with pressure, but the dominant fluctuation frequency decreased. Proper orthogonal decomposition analysis of high-speed schlieren images of the flame front was used to verify the results.

Categories: Latest papers in fluid mechanics

### Effect of gravity-induced fluid inertia on the accumulation and dispersion of motile plankton settling weakly in turbulence

Physics of Fluids, Volume 34, Issue 8, August 2022.

We investigate the effect of gravity-induced fluid inertia on motile plankton cells settling weakly through isotropic turbulence using direct numerical simulations. Gyrotaxis arises from the gravity-induced fluid inertial torque, leading to upward migration of the settling elongated micro-organisms when their swimming speed exceeds the settling speed. Preferential sampling and small-scale fractal clustering of plankton cells are studied over a wide range of swimming speeds and aspect ratios. It is found that orientation fluctuation induced by the effect of the fluid inertia and preferential alignment with turbulent strain are the most important factors affecting the statistics, which are responsible for determining the optimal shape. For strong gyrotaxis, the organisms tend to form noticeable clusters in the vertical direction. An investigation of the dispersion reveals that the fluid inertial effects contribute to the enhancement of the long-time vertical dispersion of the organisms by increasing their root-mean-squared velocity. Our results show how the fluid inertial effects can influence clustering and dispersion statistics of the organisms in turbulence, which turns out to provide an environment conducive to their survival.

We investigate the effect of gravity-induced fluid inertia on motile plankton cells settling weakly through isotropic turbulence using direct numerical simulations. Gyrotaxis arises from the gravity-induced fluid inertial torque, leading to upward migration of the settling elongated micro-organisms when their swimming speed exceeds the settling speed. Preferential sampling and small-scale fractal clustering of plankton cells are studied over a wide range of swimming speeds and aspect ratios. It is found that orientation fluctuation induced by the effect of the fluid inertia and preferential alignment with turbulent strain are the most important factors affecting the statistics, which are responsible for determining the optimal shape. For strong gyrotaxis, the organisms tend to form noticeable clusters in the vertical direction. An investigation of the dispersion reveals that the fluid inertial effects contribute to the enhancement of the long-time vertical dispersion of the organisms by increasing their root-mean-squared velocity. Our results show how the fluid inertial effects can influence clustering and dispersion statistics of the organisms in turbulence, which turns out to provide an environment conducive to their survival.

Categories: Latest papers in fluid mechanics

### Propagation of ionizing shock wave in a dusty gas medium under the influence of gravitational and azimuthal magnetic fields

Physics of Fluids, Volume 34, Issue 8, August 2022.

In this paper, a closed-form solution for an ionizing spherical shock/blast wave in a dusty gas (a mixture of an ideal gas and solid particles of micrometer size) under the influence of gravitational and azimuthal magnetic fields is derived. In the dusty gas mixture, the solid particles are continuously distributed, and the equilibrium flow condition holds in the entire flow field region. Analytical solutions in the closed form for the first-order approximation are derived for adiabatic and isothermal flows. Furthermore, for the second approximation, the set of ordinary differential equations is derived. The influence of problem parameters, such as the ratio of the density of the solid particles to the initial density of the ideal gas, the gravitational parameter, the solid particles mass concentration in the mixture, adiabatic index, and Alfvén-Mach number on the peak pressure on the blast wave, on physical variables and the damage radius of the blast wave is studied for the first-order approximation. Our closed-form solution for the first-order approximation in the case of adiabatic flow is analogous to Taylor's solution in the case of a strong explosion-generated blast wave. It is shown that the damage radius of the blast wave and the peak pressure on the blast wave both decrease with the addition of dust particles, and hence, the shock/blast wave strength decreases. It is observed that in the whole flow field region, the quantity [math] increases with an increase in the Alfvén-Mach number value, and hence, the shock decay with an increase in the Alfvén-Mach number.

In this paper, a closed-form solution for an ionizing spherical shock/blast wave in a dusty gas (a mixture of an ideal gas and solid particles of micrometer size) under the influence of gravitational and azimuthal magnetic fields is derived. In the dusty gas mixture, the solid particles are continuously distributed, and the equilibrium flow condition holds in the entire flow field region. Analytical solutions in the closed form for the first-order approximation are derived for adiabatic and isothermal flows. Furthermore, for the second approximation, the set of ordinary differential equations is derived. The influence of problem parameters, such as the ratio of the density of the solid particles to the initial density of the ideal gas, the gravitational parameter, the solid particles mass concentration in the mixture, adiabatic index, and Alfvén-Mach number on the peak pressure on the blast wave, on physical variables and the damage radius of the blast wave is studied for the first-order approximation. Our closed-form solution for the first-order approximation in the case of adiabatic flow is analogous to Taylor's solution in the case of a strong explosion-generated blast wave. It is shown that the damage radius of the blast wave and the peak pressure on the blast wave both decrease with the addition of dust particles, and hence, the shock/blast wave strength decreases. It is observed that in the whole flow field region, the quantity [math] increases with an increase in the Alfvén-Mach number value, and hence, the shock decay with an increase in the Alfvén-Mach number.

Categories: Latest papers in fluid mechanics

### Theory of sphere motions in viscous fluids including elasticity and compressibility

Physics of Fluids, Volume 34, Issue 8, August 2022.

We study the motions of an elastic sphere and a compressible fluid sphere suspended in a compressible fluid. To this end, we use a scheme of a vector representation for the velocity in hydrodynamics and for the displacement in elasticity. First, we calculate the steady-state elastic displacement of a solid sphere under a gravity and a surface-tension gradient. Second, we examine the finite-size effects in a spherical container and find bulk acoustic resonance induced by an oscillating solid sphere. Third, applying periodic forces, we calculate the displacement, the velocity field, and the frequency-dependent friction constant for an elastic sphere and a compressible fluid sphere. We find complex acoustic effects sensitively depending on the frequency.

We study the motions of an elastic sphere and a compressible fluid sphere suspended in a compressible fluid. To this end, we use a scheme of a vector representation for the velocity in hydrodynamics and for the displacement in elasticity. First, we calculate the steady-state elastic displacement of a solid sphere under a gravity and a surface-tension gradient. Second, we examine the finite-size effects in a spherical container and find bulk acoustic resonance induced by an oscillating solid sphere. Third, applying periodic forces, we calculate the displacement, the velocity field, and the frequency-dependent friction constant for an elastic sphere and a compressible fluid sphere. We find complex acoustic effects sensitively depending on the frequency.

Categories: Latest papers in fluid mechanics

### Transport properties for neutral C, H, N, O, and Si-containing species and mixtures from the Gordon and McBride thermodynamic database

Physics of Fluids, Volume 34, Issue 8, August 2022.

Accurate transport properties of non-ionized gas mixtures of C, H, O, N, and Si-containing species at temperatures up to 4000 K are essential in many scientific fields. Mixture transport properties are computed through the solution of linear transport systems, requiring collision integrals as functions of temperature for each binary collision pair in the mixture. Due to the dimensionality of the problem, no such database exists for all the 180 hydrocarbons and silicon species detailed in the nine-coefficient polynomial thermodynamic database of Gordon and McBride, widely used in many applications. This constraint was overcome by using a phenomenological inter-molecular potential energy surface suitable for transport properties, which describes the pair interaction approximated with two fundamental species physical properties, namely the dipole electric polarizability and the number of effective electrons participating in the interaction. These two parameters were calculated with ab initio quantum chemistry calculations, since they were not always available in literature. The studied methodology was verified and validated against other approaches at a species and collision integral level. Transport properties for a variety of equilibrium mixtures, including planetary atmospheres and chemical compositions of thermal protection materials relevant to aerospace applications, were calculated, assessing the predictive capabilities of this new database.

Accurate transport properties of non-ionized gas mixtures of C, H, O, N, and Si-containing species at temperatures up to 4000 K are essential in many scientific fields. Mixture transport properties are computed through the solution of linear transport systems, requiring collision integrals as functions of temperature for each binary collision pair in the mixture. Due to the dimensionality of the problem, no such database exists for all the 180 hydrocarbons and silicon species detailed in the nine-coefficient polynomial thermodynamic database of Gordon and McBride, widely used in many applications. This constraint was overcome by using a phenomenological inter-molecular potential energy surface suitable for transport properties, which describes the pair interaction approximated with two fundamental species physical properties, namely the dipole electric polarizability and the number of effective electrons participating in the interaction. These two parameters were calculated with ab initio quantum chemistry calculations, since they were not always available in literature. The studied methodology was verified and validated against other approaches at a species and collision integral level. Transport properties for a variety of equilibrium mixtures, including planetary atmospheres and chemical compositions of thermal protection materials relevant to aerospace applications, were calculated, assessing the predictive capabilities of this new database.

Categories: Latest papers in fluid mechanics

### Laser light-induced deformation of free surface of oil due to thermocapillary Marangoni phenomenon: Experiment and computational fluid dynamics simulations

Physics of Fluids, Volume 34, Issue 8, August 2022.

Remote light-induced free liquid surface deformation has been studied in various systems for decades. One of the mechanisms able to do this task is driven by the thermocapillary Marangoni effect. The strength of the light–matter interaction, which is usually weak, here is amplified by the light absorption and heat production that changes surface tension. Here, we report on an experimental study aimed at dynamical aspects of the deformation induced under conditions of chopped laser excitation light. The light-induced deformations are usually in the range of several micrometers. Therefore, we applied the interferometric technique to measure deformation profiles in real time. Experiments were performed in the shallow bath of the rapeseed oil with an azo-dye and excited with 514.5 nm and probed with 650 nm coherent laser beams, respectively. The mechanism of deformation driven by Marangoni effect was carefully modeled in 3D by computational fluid dynamic numerical simulations within the COMSOL Multiphysics package. The adaptive mesh technique used in the simulation together with solving the time-dependent coupled Navier–Stokes and heat transport differential equations allowed us to replicate the experimental findings. A satisfactory agreement between the results of the simulations and those of the experiment in terms of the dynamics, shape, and depth of the deformation has been obtained. The toroidal-like whirls accompanying the thermocapillary Marangoni effect were identified by the simulation results. We then experimentally proved that these toroidal-like vortices, which accompany laser heating in dyed oil, formed a kind of novel hydrodynamic trap, in the center of their quiet zone, in which microcrystals can be trapped.

Remote light-induced free liquid surface deformation has been studied in various systems for decades. One of the mechanisms able to do this task is driven by the thermocapillary Marangoni effect. The strength of the light–matter interaction, which is usually weak, here is amplified by the light absorption and heat production that changes surface tension. Here, we report on an experimental study aimed at dynamical aspects of the deformation induced under conditions of chopped laser excitation light. The light-induced deformations are usually in the range of several micrometers. Therefore, we applied the interferometric technique to measure deformation profiles in real time. Experiments were performed in the shallow bath of the rapeseed oil with an azo-dye and excited with 514.5 nm and probed with 650 nm coherent laser beams, respectively. The mechanism of deformation driven by Marangoni effect was carefully modeled in 3D by computational fluid dynamic numerical simulations within the COMSOL Multiphysics package. The adaptive mesh technique used in the simulation together with solving the time-dependent coupled Navier–Stokes and heat transport differential equations allowed us to replicate the experimental findings. A satisfactory agreement between the results of the simulations and those of the experiment in terms of the dynamics, shape, and depth of the deformation has been obtained. The toroidal-like whirls accompanying the thermocapillary Marangoni effect were identified by the simulation results. We then experimentally proved that these toroidal-like vortices, which accompany laser heating in dyed oil, formed a kind of novel hydrodynamic trap, in the center of their quiet zone, in which microcrystals can be trapped.

Categories: Latest papers in fluid mechanics

### A pseudopotential lattice Boltzmann model for simulating mass transfer around a rising bubble under real buoyancy effect

Physics of Fluids, Volume 34, Issue 8, August 2022.

A pseudopotential multicomponent lattice Boltzmann (LB) model that can account for the real buoyancy effect is proposed to simulate the mass transfer process around a rising bubble. The density profiles at the equilibrium state are determined based on the hydrostatic condition and the zero diffusion flux condition (the balance of chemical potential). Compared with the LB models using effective buoyancy force, the proposed model has three advantages: (1) avoiding the unrealistic distribution of gas components within the bubble due to the upward effective buoyancy force, (2) removing the undesirable diffusion process due to the application of effective buoyancy force, and (3) considering the effect of the pressure gradient on the change of bubble size. In addition, Henry's law, which can be automatically recovered from the multicomponent LB equation, is re-interpreted from the perspective of the balance of chemical potential. Simulation results showed that the diffusion flux non-uniformly distributes over the surface of a rising bubble. The diffusion zone primarily occurs at the top and the lateral side of a rising bubble, whereas the diffusion transport just below the rising bubble is much less significant than its counterpart above the rising bubble. Various bubble shapes and their corresponding diffusion zones have been obtained. Moreover, the correlation between the Sherwood number and the Peclet number derived from the simulation results is consistent with those from previous numerical results. Thus, the proposed LB model is capable of conducting a quantitative analysis of the mass transfer around a rising bubble.

A pseudopotential multicomponent lattice Boltzmann (LB) model that can account for the real buoyancy effect is proposed to simulate the mass transfer process around a rising bubble. The density profiles at the equilibrium state are determined based on the hydrostatic condition and the zero diffusion flux condition (the balance of chemical potential). Compared with the LB models using effective buoyancy force, the proposed model has three advantages: (1) avoiding the unrealistic distribution of gas components within the bubble due to the upward effective buoyancy force, (2) removing the undesirable diffusion process due to the application of effective buoyancy force, and (3) considering the effect of the pressure gradient on the change of bubble size. In addition, Henry's law, which can be automatically recovered from the multicomponent LB equation, is re-interpreted from the perspective of the balance of chemical potential. Simulation results showed that the diffusion flux non-uniformly distributes over the surface of a rising bubble. The diffusion zone primarily occurs at the top and the lateral side of a rising bubble, whereas the diffusion transport just below the rising bubble is much less significant than its counterpart above the rising bubble. Various bubble shapes and their corresponding diffusion zones have been obtained. Moreover, the correlation between the Sherwood number and the Peclet number derived from the simulation results is consistent with those from previous numerical results. Thus, the proposed LB model is capable of conducting a quantitative analysis of the mass transfer around a rising bubble.

Categories: Latest papers in fluid mechanics