Symmetric Vortex Research Articles

Generation of circular symmetric Airy vortex beams based on spin-multiplexed metasurface

Given that circular symmetric Airy vortex beam (CSAVB) was found to possess a stable central cavity and an opposing transport process to circular Airy vortex beam, it has been recognized as a potentially powerful tool for particle trapping and optical communication. In order to facilitate broader application scenarios, this paper presents a novel approach to the generation of multiple CASVBs based on a single metasurface. In the proposed method, three independent CSAVBs carrying different new kinds of power-exponent-phase vortices (NPEPVs) can be obtained under two orthogonal circularly polarized or an arbitrary linear polarized incident, respectively. Each of these vortex structures is characterized by a distinct orbital angular momentum, which is jointly determined by two parameters of the NPEPVs. This indicates that the CSAVB and the device have greater freedom than the canonical optical vortex beams and the previous vortex beam generators in controlling the optical vortex. These results have the potential to advance the development of vortex beams and enhance their applications in micromanipulation, optical communication and imaging.

Research on the Flow-Induced Vibration of Cylindrical Structures Using Lagrangian-Based Dynamic Mode Decomposition

An oscillating flow past a structure represents a complex, high-dimensional, and nonlinear flow phenomenon, which can lead to the failure of structures due to material fatigue or constraint relaxation. In order to better understand flow-induced vibration (FIV) and coupled flow fields, a numerical simulation of a two-degrees-of-freedom FIV in a cylinder was conducted. Based on the Lagrangian-based dynamic mode decomposition (L-DMD) method, the vorticity field and motion characteristics of a cylinder were decomposed, reconstructed, and predicted. A comparison was made to the traditional Eulerian-based dynamic mode decomposition (E-DMD) method. The research results show that the first-order mode in the stable phase represents the mean flow field, showcasing the slander tail vortex structure during the vortex-shedding period and the average displacement in the in-line direction. The second mode predominantly captures the crossflow displacement, with a frequency of approximately 0.43 Hz, closely matching the corresponding frequency observed in the CFD results. The higher dominant modes mainly capture outward-spreading, smaller-scale vortex structures with detail displacement characteristics. The motion of the cylinder in the in-line direction was accompanied by symmetric vortex structures, while the motion of the cylinder in the crossflow direction was associated with anti-symmetric vortex structures. Additionally, crossflow displacement will cause a symmetrical vortex structure that spreads laterally along the axis behind the cylinder. Finally, when compared with E-DMD, the L-DMD method demonstrates a notable advantage in analyzing the nonlinear characteristics of FIV.

Symmetrical vortices and laminar dust flow induced by an intense electron beam interacting with a strongly coupled dusty plasma

A strongly coupled quasi-two-dimensional dusty plasma confined electrostatically in the plasma sheath of a radio frequency (RF) plasma is irradiated by a collimated and mono-energetic pulsed electron beam (e-beam) with an energy of 13 keV and a high peak current per pulse of 30 mA. A stream of rapidly moving charged dust particles is created inside the dust crystal due to the drag force of the electrons in the e-beam. The dust flow is split into two symmetrical branches when it reaches the boundary of the round dust crystal, each following the limit of the circular confining region. This results in the formation of a double vortex flow pattern with the dust particles being transported along the irradiation direction and then aside, eventually back to the entrance position of the e-beam. The observed flow regime is laminar at all times, with the speed in the central region increasing up to 12 mm s−1 in the first 200 ms and then diminishing gradually to a steady value of about 5–6 mm s−1 during a stress relaxation time period of 360 ms. The vorticity follows a similar trend with peak values −3.8 and 3.8 s−1 and steady state values between −2.5 and 2.5 s−1 in the two symmetrical vortices. Time-resolved particle-image-velocimetry and particle-tracking-velocimetry are used to characterize the flow. Molecular dynamics simulations confirm qualitatively the experimental observations showing dust stream and double vortex formation.

Two-dimensional spanwise flow regime influenced by tip vortex around a ground-mounted square cylinder in low turbulence uniform flow

The time series data of the lift force acting on a ground-mounted square cylinder in low-turbulence uniform flow reveal a distinctive pattern characterized by a predominant high-amplitude process modulated by intermittent low-amplitude fluctuations. This behavior arises from the intricate interplay between tip and Kármán vortices. However, conflicting interpretations persist, with some findings even presenting contradictory conclusions, particularly regarding the presence of symmetric shedding in the fluctuating lift force process with low amplitude. Furthermore, a clear consensus regarding the mechanism governing the interaction between the tip vortex and the spanwise vortex remains elusive. This study aims to elucidate the two-dimensional flow regime in the spanwise direction influenced by the tip vortex of a ground-mounted square cylinder in low-turbulence uniform flow through experimental investigation. Multiple-point synchronous pressure measurement and particle image velocimetry systems are utilized to measure wind pressure on the side walls and the corresponding flow field at 2/3 of the cylinder's height. The analysis confirms the presence of two distinct types of lift force coefficient behavior: low-amplitude fluctuation (LAF) characterized by longer durations and high-amplitude fluctuation (HAF) occurring in shorter intervals. Subsequently, the flow regime in the near wake corresponding to each mode of the lift force coefficient is discussed. It is observed that the LAF regime corresponds to symmetrical vortex shedding with a prolonged shear layer, maintaining nearly constant curvature. Conversely, for HAF, a pronounced Kármán vortex street is evident. This study conclusively demonstrates the existence of symmetrical vortex shedding, which predominantly contributes to the LAF component of the lift force.

Hydrodynamic behavior and routing problem of an undulated biomimetic beam in flow environments

Undulated biomimetic propulsion has gained an extensive attention with upsurge of bionic applications. However, its performance in different flow environments is rarely discussed. In this paper, hydrodynamic behavior of an undulated beam in flow environments is studied, as well as its routing problem. The previously proposed loosely coupled partitioned algorithm is adopted. Motion of an undulated beam in still water is simulated to validate this algorithm. And then, hydrodynamic behavior of beam in flow environments with different directions and velocities is studied. It is found that velocity of beam is linearly affected by longitudinal flow and symmetric vortex structure still keeps. While transverse flow leads to the unequal amplitudes of velocity valley and crest, and symmetric vortex structure is lost. The influence of oblique flow could be regard as the combination of longitudinal and transverse flow components. Flow details are analyzed to reveal the mechanism of those hydrodynamic changes. Transverse flow component plays an important role. It significantly changes the pressure difference around beam and promotes the mixture of vortex. Besides, performance of beam in different flows and routing problem indicate that the straight path between the beginning and ending points is not always the best choice.

An experimental investigation of constrained melting of a phase change material (PCM) in circular geometries, part I: Velocity characterization

This study is focused on the detailed characterization of the transient velocity fields of a phase change material (PCM) enclosed in a geometry with a circular cross-section subjected to uniform external heating. Particle image velocimetry (PIV) was used to study the velocity behavior related to the buoyancy-driven convection. The PCM was initially subcooled, and the walls suddenly heated to exceed the melting temperature. Experiments were conducted using Rubitherm RT26 in a quasi-2D circular enclosure at three applied heating conditions. Detailed velocity fields show strong symmetric convective vortices at the sides of the PCM chamber, and a three-dimensional recirculation was detected near the bottom. These structures strongly influence the melting behavior. The results suggest self-similarity in flow behavior between heating conditions. Detailed transient temperature fields and an extended discussion of the associated heat transfer behavior are presented in the companion paper (Part II).

Multipole solitons and vortex solitons in nonlocal nonlinear media

The nonlinear Schrödinger equation (NLSE) under nonlocal nonlinear media (NNM) is described and the approximate analytical solutions of the vector multipole solitons and vortex optical soliton clusters are obtained via the variational method. The results show that the structure of the optical solitons is determined by modulation depth and topological charge. In the propagation process, the spatial soliton has an observable rotation property. Under certain conditions, the rotating space modulated vortex optical solitons degenerate into circular symmetric vortex optical solitons. The results can be extended to other physical systems.

Molding the acoustic cavity–analyzing the influence of toroidal vortex development on acoustic multi-bubble macrostructures under different ultrasonic horn tip diameters

The acoustic cavity structure typically experiences a sequence of transfigurations during its sinusoidal growth–collapse cycle. However, upon examining the cavity structure in aqueous bodies, it appears that the growth structure attained falls between two geometrical structures, namely, mushroom-like structure (MBS) and cone-like bubble structure (CBS), based on the actuated ultrasonic horn tip diameter. With the recurring observations of the emergence of proximal toroidal vortices, the present investigation conducts a numerical analysis exploring the vortex development under 3, 6, 13, 16, and 19 mm horn tips to establish a potential correlation between the vortex and the cavity structure. The study presents a computational fluid dynamic investigation to capture the nature of the vortex evolution, in terms of size and position, and its respective cavitation development. The first indicator of potential correlation was the equivalency of the vortex expansion–contraction frequency and the cavity's sub-harmonic frequency. It has been found that the cavity structure is molded into MBS by the presence of a symmetric locomotive vortex structure that extends up to 1.5 times the horn tip diameter. Meanwhile, CBS is observed to take shape in the presence of an eccentric locomotive vortex that attains a size within 0.2–0.6 times the horn tip diameter. The significance of the vortex size and position is also observed in the cavity's collapse, as the vortex appears to govern the ability of the cavity impinging jet to initialize the collapse phase.

Abruptly autofocusing of polycyclic tornado symmetric Pearcey vortex beams in the fractional Schrödinger equation

In this paper, we study polycyclic tornado symmetric Pearcey (PTSP) vortex beam induced by superimposing spiral phase and vortex, and its propagation dynamics in the fractional Schrödinger equation (FSE). We find that the autofocusing of the symmetric Pearcey beam is enhanced and the autofocus length is shorten with the increase of Lévy index α. Polycyclic tornado phase will form a dark tornado ring (DTR) on the basis of PTSP vortex beam, and the radius of the DTR will also change with the increase of the propagation distance. Finally, the divergence force and gradient force of the PTSP vortex beam in FSE are displayed during transmission. The development of these special properties in FSE has important implications for optical tweezers, medical and military applications.

Spatiotemporal optical vortex reconnections of multi-vortices

Vortex reconnections are ubiquitous events found in diverse media. Here we show that vortex reconnections also occur between spatiotemporal vortices in optical waves. Since vortices exhibit orbital angular momentum (OAM), the reconnections of optical vortices create a variety of connected OAM states. Dispersion and diffraction can cause different reconnection pairs, depending on the orientation of the vortices. The transverse crossing of two vortices with a topological charge of one can produce unique vortex loop reconnection patterns. Higher topological charges result in arrays of vortex loops and connection points. Crossing of three vortices produces spherical structures made of three symmetrical vortex arms. A three vortices reconnection with higher topological charges develops complicated patterns similar to turbulence cascade phenomena in other media. Studying optical vortex interactions may bring insight into vortex reconnections in other fields. We also provide experimental results of two-vortex loop interaction.

Flow over a single dimple recessed in a flat plate

Direct numerical simulations have been conducted to investigate a zero-pressure-gradient boundary layer flow over a single shallow dimple. Here, the dimple depth to dimple diameter ratio (d/D) as well as the Reynolds number (based on D and free-stream velocity) are fixed at 0.05 and 20 000, respectively. The effect of inlet boundary layer thickness δ on a given dimple is investigated by considering δ/D∈[0.023,0.1]. The flow within the dimple exhibits either a horseshoe vortex (a continuous core line through the two spirals within the dimple) or a tornado-like vortex pair (discontinuous core line). For the given parameter range, four different flow patterns have been identified within the single dimple: (i) a steady symmetric horseshoe vortex pattern for δ/D∈[0.053,0.1], (ii) a steady asymmetric horseshoe vortex pattern for δ/D=0.04, (iii) a quasi-periodic asymmetric horseshoe vortex pattern for δ/D=0.033, and (iv) a mixed horseshoe and tornado-like vortex pattern for δ/D=0.023. The growth of the streamwise vorticity, mainly caused by the tilting of the vertical vorticity, plays a key role in the transition between the different flow patterns. Dimple-induced velocity streaks above the single dimple have been investigated in detail for the first time, showing four different streaks: (i) a high-speed streak above the dimple, (ii) two side-low-speed streaks located outside the dimple span, (iii) two side-high-speed streaks, and (iv) a mid-low-speed streak in between them. These are mainly caused by a flow acceleration effect and a flow diffuser effect over the dimple, as well as a “lift-up” mechanism within the downstream part of the dimple, tilting the boundary layer upward.

Turbulent flow in an I–L junction: Impacts of the pipe diameter ratio

Pipeline junction plays a pivotal role in fluid mixing for biomedical, chemical, and industrial processes. This study introduces an I–L junction for pipeline systems, fostering concurrent flow between branch-pipe injection and the main pipe bulk flow. In contrast to the conventional T-junction with perpendicular injection, the I–L design demonstrates high potential in mitigating vibration-induced fatigue risks, given an optimal branch-to-main pipe diameter ratio, rd. Using unsteady Reynolds-averaged Navier–Stokes equations, the study assesses fluid mixing across a broad range of rd (1/12–1/2.5). The streamline geometry undergoes a transition from well-defined symmetric vortices to unsteady oscillations when the pipe diameters diverge beyond 1/4, arising from vortex shedding in the wake of the branch pipe. Despite the conventional T-junction showing a more homogeneous velocity distribution in the streamwise direction, its turbulent kinetic energy (TKE, both modeled and calculated from the resolved-scale velocities) near the junction is an order of magnitude larger, implying high overall inhomogeneity in the flow. The TKE decays rapidly to an equivalent level compared to the proposed I–L junction approaching discharge, indicating that the peaking of TKE in the T-junction does not significantly contribute to enhanced fluid mixing. Conversely, it can likely result in harmful vibrations inside the pipeline. While the turbulence statistics remain qualitatively unchanged for rd<1/4, an enlarged discrepancy in pipe diameters beyond rd<1/6 yields more favorable mean surface pressure coefficient, CP¯. The results provide insights into pipeline design, recommending an optimal pipe diameter ratio for enhanced mixing of successively collected fluids while retaining improved system reliability.

Thermohydraulic performance analysis and parameters optimization of the combined heat sinks with microchannels and micro pin-fins

The combined heat sinks of microchannels and micro pin-fins are numerically studied in depth by three-dimensional conjugate heat transfer models for flow rate (Qv) ranging from 18 to 90 ml/min. The influence degrees of multiple parameters, i.e., the lengths and widths of the cavities and pin-fins, on cooling effect, pressure drop and comprehensive performance are analyzed quantitatively by Taguchi method. And the optimal combination structures for temperature of heat sink (OCS-T), pressure drop (OCS-PD) and performance evaluation criterion (OCS-PEC) are obtained accordingly. The original heat sink with fan shaped cavities and diamond pin-fins (FC-DPF) and the smooth rectangular heat sink (SR) are selected for comparison. The coupling effects of four structure parameters on the local and average thermal hydraulic characteristics are elucidated. The interrelation of multiple physical fields and the comprehensive efficiency of the optimal combination structures are discussed thoroughly. Moreover, the thermodynamic properties and irreversibility are illustrated based on the entropy generation. Results demonstrate that the length of fan shaped cavity and the width of diamond pin–fin have a dominant impact on heat dissipation and pressure drop. The width of cavity has a noticeable impact on the overall performance. Large width of cavity is favorable to induce transverse flow, and large width of pin–fin contributes to distinct vortices. The symmetrical vortices in the direction of channel height can improve chaotic mixing and temperature uniformity. At high flow rate, the performance evaluation criterion (PEC) of the OCS-PEC is increased by 29 % compared to the original structure FC-DPF. When total thermal resistances of the above two heat sinks are similar (0.43 K/W of the OCS-PEC and 0.45 K/W of the FC-DPF), the pumping power of the OCS-PEC (0.47 W) is 35 % lower than that of the FC-DPF (0.72 W) proving the excellent overall efficiency. In addition, the OCS-PD and OCS-PEC show better thermodynamic performance and less irreversible loss for high flow rate, which implies the energy efficiency advantage. The synergistic mechanism of flow and heat transfer is revealed and the results are significant for further understanding the rules of performance enhancement. The excellent overall performance of the OCS-PEC at high flow rate makes it more promising in application for electronic chips cooling in aerospace, defense and communication fields, thermal management of battery, hydrogen storage, fusion energy management, etc.

Numerical simulation and coupling mechanism study of acoustic-inertial micromixer

Acoustic-inertial micromixers exhibit a wider operating range and higher mixing efficiency than conventional mixers. We have carried out experimental studies and numerical simulations of acoustic-inertial micromixers. It is found that the acoustic streaming will be changed in morphology and intensity by the background flow, and the coupling mechanism between them is obtained. Specifically, we developed the numerical model of acoustic-inertial micromixer by using perturbation theory and the Generalized Lagrangian Mean (GLM) theory. By dividing the flow variables into zero-order, first-order and second-order variables, we obtained the control equations representing background flow, acoustic response and time-averaged streaming flow. Then realized the decoupling analysis of the acoustic-inertial coupling phenomenon. It is found that in terms of acoustic streaming flow, the intensity extreme of it increases as the background flow rate increases. The flow velocity at 5Vpp can reach 0.46 m/s under 500 μL/min, which is 30 times for the same condition under 10 μL/min. However, the streaming morphology no longer behaves as a symmetric vortex distributed on both sides of the sharp edge, which is stretched and twisted by the background flow and structure at a high flow rate. The percentage of acoustic contribution at different working conditions is also investigated quantitatively, and the acoustic contribution index (ACI) will generally decrease to less than 0.5 after the background flow dominates the flow field. The results of the study can provide a reference for the design of acoustic-inertial micromixers with larger flow ranges and higher efficiencies.

Numerical simulation for axis switching of pulsating jet issued from rectangular nozzle at low Reynolds number

Axis switching of a jet ejected from a rectangular nozzle affects flow mixing characteristics. To elucidate such a mixing mechanism, the axis switching and vortex structure deformation should be investigated in detail. This study performed a numerical analysis of the axis switching of a pulsating jet ejected from a rectangular nozzle at a low Reynolds number. At all aspect ratios, a rectangular vortex ring similar to the shape of the nozzle cross-section is periodically shed downstream, and the side of the vortex ring deforms into a hairpin shape downstream. A vortex pair is generated inside the vortex ring downstream of the nozzle corner. When the aspect ratio is AR = 1.0, the vortex pair consists of symmetrical vortices, while as AR increases, the asymmetry of the vortex pair enlarges. At AR = 1.0, regeneration of a vortex ring occurs downstream. For AR = 2.0, alternately on the long and short sides of the nozzle, an upstream vortex ring overtakes a downstream vortex ring. Regardless of AR, downstream near the nozzle, as the vortex pair existing inside the vortex ring distorts the vortex ring, the positions of the side and corner of the vortex ring exchange, resulting in a 45° axis switching. For AR > 1.0, further downstream, the hairpin part of the vortex ring on the long side develops away from the jet center compared to the short side, causing a 90° axis switching. As a result, high turbulence occurs over a wide area, strengthening the mixing action. As AR increases, intensive interference between the vortex rings on the upstream and downstream sides diffuses the vortices downstream. Then, as turbulence by the diffused vortices widely occurs, the mixing effect is further strengthened.

A novel exploration of how localized magnetic field affects vortex generation of trihybrid nanofluids

Abstract Nanofluidics have better thermal properties than regular fluids, which makes them useful for heat transfer applications. This research investigated the complex dynamics of confined magnetic forces that influence the rotation of nanostructures and vortex formation in a tri-hybrid nanofluid (Ag, Al2O3, TiO2) flow regime. The study shows that the magnetic field can change the flow and heat transfer of nanofluidic, depending on its direction and strength. The study also provides insights into the complex physics of nanofluid flow and heat transfer, which can help design devices that use nanofluids more efficiently for cooling electronics, harvesting solar energy, and generating power from fuel cells. We used a single-phase model to model the nanofluids while the governing partial differential equations were solved numerically. An alternating-direction implicit approach has been employed to analyze the impact of confined magnetic fields on the nanofluid flow and thermal properties. Unlike previous studies that assumed uniform magnetic fields, we introduced multiple confined magnetic fields in the form of horizontal and vertical strips. Using our custom MATLAB codes, we systematically examined various parameters, including the magnetic field strength, number of strips and their position, and nanoparticle volume fraction, to assess their effects on nanofluid flow and thermal characteristics. Our findings revealed that the confined Lorentz force induced the spinning of tri-hybrid nanoparticles, resulting in a complicated vortex structure within the flow regime. In the absence of a magnetic field, a single symmetric vortex can be seen in the flow field. However, the introduction of magnetic sources stretches this vortex until it splits into two smaller, weaker vortices in the lower cavity, rotating clockwise or counterclockwise. Furthermore, the magnetic field strength significantly reduces both skin friction and the Nusselt number, while Reynolds numbers mainly affect the Nusselt number.

Micro-particle aggregation using vortices induced by vibration of a piezoelectric cantilever beam-probe structure

Large-scale nondestructive aggregation of micro-particles is essential for cell detection, microplastics removal and micro- and nano pharmaceuticals. To achieve this goal, this work proposes a method by creating a vortex region in the fluid field using low-frequency oscillation of a piezoelectric cantilever beam probe structure. Vibration of the probe agitates the liquid, creating a horseshoe-shaped vortex in the fluid field. This facilitates the movement of micro-particles and traps them. Using polystyrene microspheres with a diameter of 20 µm and pollen (20–40 µm) as aggregated objects, particle agglomeration tests and flow field PIV tests are performed. Experimental results confirm that the designed structure has the best performance with a driving voltage of 100 V and a driving frequency of 72 Hz. The maximum aggregation area of polystyrene and pollen is 106956 µm2 and 234750 µm2. There are symmetrical large vortices regions on both sides of the probe and small vortices zero vorticity near the free end of the probe. It is also confirmed that small vortices are the root cause of microparticle aggregation. The aggregation method proposed in this study has advantages of low cost, non-selectivity of characteristics for controlled samples, large manipulation area and low power consumption (0.42 W).

Investigation on the Intensification of Supertyphoon Yutu (2018) Based on Symmetric Vortex Dynamics Using the Sawyer–Eliassen Equation

This study used the revised Sawyer–Eliassen (SE) equation, taking the relaxed thermal wind balance into account, to chart the development of Supertyphoon Yutu (2018) based on symmetric vortex dynamics. The mean vortex and associated forcing sources for solving the SE equation were taken from three-dimensional numerical simulations using the ocean-coupled HWRF. The SE solutions indicate that the induced transverse circulation is sensitive to the static stability of the mean vortex, which can be significantly underestimated when the static instability is greatly increased. The impacts on the SE solution, caused by the agradient imbalance and nonhydrostatics, were not significantly large in the troposphere. Moreover, the impact of numerical residue in the tangential wind tendency equation mainly occurred in the upper troposphere, below a height of 18 km, and near the lower eyewall. Furthermore, the structural misplaced change in the forcing source may have caused a more disorganized induced transverse circulation, whereas the collocated intensity change only resulted in a proportional enhancement during the same phase. During the rapid intensification of Yutu, the tangential-wind velocity tendency, caused by the revised SE solution, was close to the actual nonlinear tendency; however, the lowest boundary layer exhibited stronger turbulent friction. The mid- to upper-tropospheric vortex intensification inside of the eyewall and outside of the eyewall can mainly be attributed to the mean and asymmetric horizontal advection and vertical advection, respectively; conversely, most of the spindown that occurred in the eyewall was caused by the mean and asymmetric horizontal advection. At lower levels, the vortex intensification near the inner eyewall was mainly induced by the effects of asymmetric vertical advection.

Conjugate Heat Transfer Characteristics of a Film-Cooled Turbine Blade Leading Edge With Staggered-Oblique Impinging Jets

Abstract The turbine blade leading edge is subjected to harsh conditions due to high heat loads and unfavorable compact structures. To improve the cooling performance, a novel impingement scheme is proposed to be used in a film-cooled turbine blade leading edge. Different from a normal impingement scheme, the novel scheme consists of two rows of staggered impinging jets at oblique angles of ±35 deg, and is thus named as the staggered-oblique impingement scheme. A conjugated numerical investigation is carried out to illustrate the underlying mechanisms of the cooling performance. Three typical jet Reynolds numbers, 6000, 12,000, and 18,000, are studied using the validated SST k–ω turbulence model. Numerical results show a flow separation within the staggered-oblique impinging jets, which causes the discharge coefficient for the novel impingement scheme lower than that for the normal impingement scheme. Results also reveal a phenomenon difference that two symmetric vortices are induced by each normal impinging jet, while only one vortex appears on the acute angle side along with each staggered-oblique impinging jet. The flow fields of the staggered-oblique impingement scheme create a more uniform heat transfer distribution and a maximum of 23.7% higher area-averaged Nusselt number than the normal impingement scheme. The area-averaged overall cooling effectiveness for the staggered-oblique impingement scheme is higher than the normal impingement scheme by a maximum of 4.8%. The uniformity and the enhancement of the overall cooling effectiveness arise from the wall jet being fully developed and affecting a larger area of the target wall. The adiabatic cooling effectiveness is similar for both impingement schemes. This indicates that the improvement in overall cooling effectiveness for the staggered-oblique impingement scheme mainly arises from internal heat transfer.

Force decomposition on flapping flexible plate via impulse theory and dynamic mode decomposition

Dynamic mode decomposition (DMD) is a widely used method to extract dynamic information from sequential flow data, aiding our comprehension of fluid dynamics and transport processes. While DMD can unveil internal system laws and predict unsteady flow phenomena, the connection between DMD modes and the nonlinear hydrodynamic behavior of solid bodies remains unexplored. This study investigated the internal relationship between DMD modes and their impact on hydrodynamic forces. We employed a penalty-immersed boundary method to simulate the behavior of a flapping flexible plate in a uniform incoming flow, generating extensive datasets of vorticity fields. By applying DMD to these datasets, we identified key modes governing the flow dynamics, including the shear layer, symmetric vortex street, and antisymmetric vortex street. Furthermore, we utilized the impulse theory to analyze the force characteristics of the plate based on the corresponding DMD modes. The net force is determined by the combined contributions of the impulse force and the vortex force. Our findings reveal that the net horizontal force is primarily influenced by the first two modes. Specifically, mode 1, characterized by a dimensionless frequency of f*=0, contributes to thrust, whereas mode 2, with f*=1, contributes to drag. This physical investigation holds relevance for fluid–structure systems involving the interaction dynamics of flexible structures with unsteady wake vortex systems.