Streamwise Vortices Research Articles

Improving the combustion of scramjet engines with struts using grooves and bumps

Grooves and bumps are arranged on both sides of a normal strut (NS) to fabricate vortex generators, and introduce streamwise vortices. Struts with sawtooth grooves (GS-1), rectangular bumps (BS-1), and trapezoidal and triangular bumps (BS-2) have been proposed. In this study, struts with V-shaped grooves (GS-2) and trapezoidal and triangular bumps (BS-3) were configured. The flow fields in the cold and hot states of scramjet combustors with NS, GS-1, GS-2, BS-1, BS-2, and BS-3 were simulated numerically using steady RANS equations and an SST k-ω turbulence model. The results show that proper arrangement of the grooves and bumps on the strut can improve the mixing and combustion performance. Compared with the NS, for GS-1, GS-2, BS-1, BS-2, and BS-3, the distance required to achieve 100% fuel mixing efficiency is shorter by 21.2%, 9.1%, 18.2%, 12.1%, and 15.2%, respectively, and to achieve 100% combustion efficiency, the distance is shorter by 42.7%, 46.9%, 47.9%, 53.1%, and 58.3%, respectively. Therefore, improvement in combustion performance does not positively correlate with improvement in the mixing performance. Large-scale heat and mass convection in streamwise vortices play a dominant role in mixing. The larger the proportion of the fuel area affected by the streamwise vortices, the more conducive it is to achieving a higher mixing performance, whereas the wall has a negative impact. However, the large-scale heat and mass convection in the streamwise vortices and small-scale heat and mass convection in the high-turbulence zones are closely related to the supply of oxygen and fuel required for the combustion zone. Large-scale streamwise vortices combined with thick high-turbulence zones are conducive to achieving a high combustion rate. When the recirculation zone has a larger combustion area and smaller wall effects, a higher combustion performance is easily achieved. Compared with the grooves, the stronger disturbance effect of the bumps on the fluid effectively increased the thickness of the high-turbulence zone, thus obtaining a higher combustion performance. However, the greater blocking area and new oblique shockwaves generated by the bumps induced a greater total pressure loss. Therefore, combining bumps and grooves can further optimize strut configurations.

Turbulent/non-turbulent interface of the turbulent boundary-layer over a spanwise-heterogeneous converging/diverging riblets rough wall

Turbulent boundary layer (TBL) flows over various spanwise-heterogeneous rough walls exhibit spanwise variations in turbulence statistics, implying modifications of the turbulent/non-turbulent interface (T/NTI). In this work, based on the datasets of TBL flows over a spanwise-alternating converging/diverging riblets wall, we investigate behavior of T/NTI, properties of ‘bubble’ and ‘drop’ that are associated with T/NTI, as well as connections between T/NTI and large-scale structures within the boundary layer. The flow datasets were obtained through stereoscopic particle image velocimetry measurements on the cross-stream plane of the TBL flow at a Reynolds number Reθ = 1.3 × 104. The T/NTI and associated ‘bubble’ and ‘drop’ are identified using a kinetic energy criterion, while the large-scale structures by a streak detection algorithm. It is observed that the T/NTI height and the occurrence of ‘bubble’ and ‘drop’ display a spanwise-heterogeneous feature, with lower T/NTI height and higher occurrence probability of ‘bubble’ over the diverging section of riblets than over the converging section of riblets. Results of conditional average show that the ‘bubble’ is associated with positive streamwise fluctuations, common-down flow and a pair of counter-rotating streamwise vortices, while the ‘drop’ with negative streamwise fluctuation, common-up flow and a pair of counter-rotating streamwise vortices. Probability density functions of the ‘bubble’ size and fractal dimensions of the T/NTI are found similar for both the riblets and smooth wall flows. Furthermore, it is observed that the large-scale low-speed structures occurring preferentially over the converging section of riblets play a role in elevating T/NTI while the large-scale high-speed ones over the diverging section of riblets lowering down T/NTI.

Heat Transfer and Flow Characteristics of Channel Impingement Cooling Structure at Leading Edge Inside Turbine Blades Using Large Eddy Simulation

Abstract As a main part of multichannel wall jet cooling structure, channel impingement cooling is a cooling strategy of great concern at the leading edge inside of the turbine blade. In this paper, heat transfer and flow behavior in the channel impingement cooling structure are investigated by large eddy simulation (LES). The results imply that impingement created by curvature-induced centrifugal instabilities in the turning region of the cooling channel is dominated by a streamwise vortex system containing a counter-rotating Dean vortex, which presents high heat transfer streaks along the streamwise direction on the target wall. The intensely unsteady nature of the cooling jet induced by a lack of equilibrium between the pressure gradient and the centrifugal force is precisely captured herein by LES. An attaching-wall jet formed on the outer wall downstream of the cooling channel has highly three-dimensional characteristics not observed by Reynolds-averaged Navier–Stokes equations (RANS). Heat transfer augmentation on the target wall of the cooling channel is mainly due to the intensifying streamwise vortex system developing in the turning region as driven by the centrifugal force. This research work will provide a reference for the optimization and application of multichannel wall jet cooling for gas turbine blades.

Shock-induced supersonic combustion with a streamwise vortex

Two hypermixer fuel-injector struts, which can induce streamwise vortices in the middle of a combustor, are used to investigate numerically how the difference of vortex circulation affects the interaction of a streamwise vortex with shock-induced combustion at a Mach number of 3.5. Hydrogen fuel is injected into a combustor at a jet Mach number of 1.5 from the rear of the struts. The separation-restraint (SR) struts used here are SR1 and SR2 with a smaller vortex circulation. Supersonic combustion starts at the point where the reflected oblique-shock waves impinge on the streamwise vortex, and the formed streamwise vortex interacts with the reflected shock waves twice. Although weak vortex breakdowns occur due to the second shock interaction for both struts, strong breakdown that occurs as a result of the first shock interaction appears only in the case of SR1. In terms of vortex breakdown connected with combustion, our results demonstrate that high pressure rises occur close to the vortex breakdown, which can be identified by the integrated helicity, the enstrophy calculated by subtracting the streamwise component, and the occurrence of the subsonic region. In addition, we found that the combustion efficiency of SR2 without strong vortex breakdown was higher than that of SR1. This can be understood by dividing the cross section perpendicular to the main flow into two distinct regions, namely the strut region and the outside region. Although there was little difference in the efficiency calculated on the strut region including the vortex, between the two struts, SR2 was found to be more efficient in the outside region. Therefore, circulation could significantly influence combustion with a streamwise vortex using hypermixer struts.

Investigation of pulsed direct-current plasma jets in a turbulent boundary layer

Characteristics of the plasma jet produced by a pulsed direct-current (pulsed-DC) dielectric barrier discharge (DBD) and its interaction with a turbulent boundary layer (TBL) are investigated in detail using stereo particle imaging velocimetry. Quiescent-flow characterization results show that a positive starting vortex and a negative near-wall jet structure are induced by the pulsed-DC DBD plasma actuator. With increasing pulse width and discharge frequency, the jet velocity magnitude increases monotonously, as a direct result of the extension of fluid particle acceleration time. During the interaction with a cross-flow TBL, two streamwise vortices with opposite signs are observed at the two sides of the electrode junction, which essentially originate from the starting vortex and negative jet in quiescent air. The skin-friction drag variations are dominated by the cross-stream momentum transportation of streamwise vortices, with drag reduction in the vortex upwash zone and drag increase in the downwash zone. Compared with the conventional alternating-current DBD plasma actuators, the turbulent fluctuations produced by pulsed-DC DBD are much higher, which also affects the skin-friction drag. Further proper orthogonal decomposition (POD) analysis reveals that two distinctly different flow patterns are produced by pulsed-DC DBD working at small and large pulse widths. The dominant POD modes causing the most velocity fluctuation are the spanwise translation and deformation of plasma-induced streamwise vortices. These results provide insights into the basic phenomenon of pulsed-DC plasma jets in cross flow, which recently has demonstrated its promising applications in turbulent skin-friction reduction.

The evolution of second harmonic waves in oblique transition

The evolution of second harmonic waves in oblique transition

Mechanisms of Characteristic Parameters of Plasma Actuator on Film Cooling and Turbulent Transport Based on Multi-Objective Optimization

In this paper, film cooling effectiveness and pressure loss coefficient are taken as the objective functions to optimize the plasma characteristic parameters such as electrode position, spacing, length and actuation intensity for enhancing film cooling performance. Regression equations of two objective functions are accessed by the Response Surface Method, and Non-Dominated Sorting Genetic Algorithm is applied for bi-objective optimization. Two sets of Pareto optimal solutions are available via the Technique for Order Preference by Similarity to an Ideal Solution decision method. Pareto optimal solutions are calculated by Detached Eddy Simulation to clarify the turbulent transport and heat transfer characteristics induced by the plasma. Wall-averaged cooling effectiveness and pressure loss coefficient without plasma power supply are 64.3% and 3.9% superior to that without electrode, respectively. The plasma fragments the hairpin vortex into a striped structure and induces a large scale streamwise vortex behind the bare electrode. The plasma weakens the velocity diffusion and turbulent heat transport in the ionization zone. Overlapping electrodes render the root-mean-square pulsation velocity and Reynolds stress of the optimal model 1 both less than those of the optimal model 2 without overlapping electrodes, and flow field disorder is decreased. Electrode position interferes with the action location of plasma on cooling jet. Actuation intensity affects the ionization intensity and has a maximum value of 8.88 to optimize the actuator performance. Compared with no plasma actuation, wall-averaged cooling effectiveness of optimal model 1 and optimal model 2 are enhanced by 30.7% and 21.8%, and pressure loss coefficient are declined by 7.7% and 7.1%, respectively.

Dynamic Analysis of Tip Leakage Phenomena in Axial Flow Pumps Using a Square-Cavity Jet Model

In the field of pump impeller studies, tip leakage flow (TLF) and the resultant tip leakage vortex (TLV) significantly influence hydraulic efficiency, cavitation, and noise generation. This paper builds a novel square-cavity jet model combined with Large Eddy Simulation (LES) technology to obtain precise the dynamic properties of the TLV, significantly simplifying the computational resources required for numerical simulations. The novel square-cavity jet model simplifies a single blade channel to a square-cavity, and then adds a longitudinal slit on the top wall of the square-cavity. The analysis of both instantaneous and time-averaged flow fields indicates that the interaction between the main flow and the jet is the primary source of TLV generation. This study successfully captures the formation process of the TLV and accurately reveals its turbulent coherent structures. The evolution of the TLV is divided into three main parts: the first part is the jet slot, predominantly characterized by negative vorticity flow. The second part is the TLV formation, which is mainly composed of significant negative streamwise vortices. The third part is the development of the TLV, where positive and negative vorticities begin to interact, resulting in a more complex overall structure. The entire evolution of the TLV phenomenon starts with a concentrated negative vortex, which, after breakdown, develops at a certain angle to the slot and continuously advances towards the sidewall, ultimately resulting in the formation of a large-scale intermingled group of small-scale positive and negative vortices. This research not only provides a new physical model for investigating the tip leakage phenomenon in axial flow pumps but also offers a powerful tool and methodology for future studies in similar complex flow domains.

Turbulent spot formation in stably stratified three-dimensional Yukawa liquids

A plane-Couette flow (PCF) is considered in a stably stratified three-dimensional (3D) Yukawa liquid, perturbed initially with a finite amplitude 3D perturbation. Stable stratification in density is achieved by subjecting the medium to external gravity. We demonstrate turbulent spot formation in a stably stratified PCF. The dynamics of the system is shown to depend upon the value of κ, which is associated with the range of interaction. We have performed “first principles” classical 3D molecular dynamics (MD) simulations for “hypergravity” (1.3g0, g0 is Earth's gravitational force for unit mass in our normalized unit) and “milligravity” (9×10−3g0) cases for κ, 1.0 and 4.0, respectively. We extract relevant fluid quantities from MD data. For the hypergravity case, when the system is evolved in time under stable stratification, the kinetic energy is observed to deposit in the lower wave vectors (Kx, Kz), leading to “inverse cascade” in the plane perpendicular to the direction of stratification. As a result, we observe large-scale structure formation in velocity and streamwise vorticity fields. Nucleation of velocity streak is observed for the first time in the stably stratified case in our simulation. The coherent structures in the velocity and streamwise vorticity fields are found to sustain for longer period of time for the stably stratified cases as compared to the unstratified case. For the milligravity case, the large-scale dynamics is observed to enhance. Unlike unstratified PCF, a background flow in Y-averaged streamwise fluid velocity field is observed for the stably stratified case. We believe that our results using “first principles” classical MD simulations on subcritical turbulence in stably stratified Yukawa liquid, may have ramifications to wider class turbulence problems. Published by the American Physical Society 2024

Experiments on Cavitation Control around a Cylinder Using Biomimetic Riblets

Experimental investigations were conducted to uncover the impact of cavitation control—through the use of biomimetic riblets on cavitating flows around a circular cylinder. First, the dynamics of cavitation in the flow behind a finite cylinder (without riblets) was unveiled by visualizing the cavitation clouds and measuring the lift force fluctuations acting on the cylinder. Second, in a significant step forward, a comprehensive explanation was provided for the cavitation control methods using two bio-inspired riblet morphologies positioned in different orientations and locations on the cylinder. For the first time, the impacts of these tiny formations on the flow dynamics and the associated cavitation process were scrutinized. This showed that scalloped riblets, with their curved design, induced secondary vortices near their tips and distorted primary streamwise vortices, and that high velocity gradients near the jagged pattern peaks of sawtooth riblets delayed flow separation, which affected cavitation.

Introducing the Rankine vortex method for drag reduction in wall-bounded turbulent flows at low Reynolds number through streamwise vortex manipulation

It is well known that the near-wall streamwise vortices, together with the streaks, are the most important turbulent structures closely associated with drag reduction. Weakening or modifying the streamwise vortices are, thus, general approaches in near-wall turbulent control studies. In this study, a novel approach to manipulate the flow is introduced and applied to a turbulent channel flow in order to achieve drag reduction. The idea behind the “Rankine vortex method” is to generate a force based on the statistical and geometrical information of streamwise vortices. Direct numerical simulations of a turbulent channel flow at a frictional Reynolds number, Reτ, of 180 (based on the driving pressure gradient and channel half-width) are performed. The force is applied in the vicinity of the lower wall of the channel, and the results are comparatively analyzed for the cases with and without force implemented. A drag reduction of 10% is achieved. The theoretical flow control approach presented, along with the associated analysis, has the potential to enhance our current understanding of flow control mechanisms through the manipulation of near-wall turbulence.

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.

Direct numerical simulation of oblique-wave transition in concave boundary layer

Investigation of transition in a concave boundary layer is conducted via three-dimensional direct numerical simulation at Mach 3. The model consists of a flat plate and a concave plate, connected smoothly. The development of the boundary layer in the unperturbed flow is computed initially. It is found that the boundary layer thickness rapidly increases due to the separation bubble, caused by an adverse pressure gradient. Subsequently, spanwise vortices are generated by the Kelvin–Helmholtz instability, which develops within the strong shear layer. Then, a pair of oblique waves is introduced at the inlet of the computational domain through suction and blowing slot to examine the impact of oblique waves on transition and separation of the concave plate boundary layer. The investigation reveals that oblique waves significantly reduce the separation bubble and the boundary layer thickness and weaken the Kelvin–Helmholtz instability. Oblique waves generate streamwise vortices, while high-amplitude oblique waves lead to a three-dimensional checkerboard structure and staggered Λ vortices. The findings demonstrate that oblique breakdown can advance to a fully developed turbulent boundary layer, hence operating as a relevant mechanism for transition in supersonic concave boundary layers.

Mixing enhancement of transverse jets in supersonic crossflow using an actively controlled novel fluidic oscillator

This study investigates the fluid dynamics and mixing characteristics of an oscillating sonic jet injected into a supersonic cross flow of Mach 2.1 using experimental and computational techniques. The oscillating jet is produced by a novel fluidic oscillator, which consists of a primary rectangular duct that expands into an outer duct with sudden expansion. Control jets are injected in the lateral direction from the side walls of the sudden expansion in an out-of-phase manner to oscillate the injected jet in the spanwise direction of the crossflow. Experimental and numerical investigations based on wall static pressure and mass fraction fluctuations, respectively, revealed that the injected jet oscillation frequency matches the control jet frequency. The iso-surface of lambda-2 criterion showed the presence of various dominant vortex structures, such as counter-rotating vortex pairs, horseshoe vortex, sidewall vortices, and trailing vortices. Helicity contour plots showed that the streamwise vortices oscillate in the spanwise direction with the control strategy and promote the spread of the injected jet in the spanwise direction. The spatiotemporal reconstruction (z–t plot) of the density gradients at a particular streamwise location revealed that the bow shock produced by the interaction of the injected jet and the crossflow oscillates with the actuation of the control strategy. The power spectral density of the z–t plot revealed that the shock wave oscillation frequency matches the control jet frequency. The oscillating jet produced by the control strategy showed significant mixing enhancement in supersonic crossflow compared to a simple rectangular injection.

Noise mitigation in rectangular jets through plasma actuator-based shear layer control

A computational analysis is performed to study the three-dimensional response of rectangular shear layers to plasma actuator-based control, in the context of sound mitigation of supersonic non-axisymmetric jets. A Mach $1.5$ rectangular jet with an aspect ratio $2:1$ is controlled using experimentally informed actuation patterns, referred to as M0, M1, M2, M3, M ${\rm \pi}$ and M+/ $-$ 1. While the first five progressively increase the phase difference between successive actuators thus enhancing three-dimensionality of the shear layer structures, the latter corresponds to the flapping mode of the jet. A preliminary linear analysis identifies that the frequency, $St\sim 1$ , has a relatively high overall amplification within the baseline shear layer, and is hence utilized for control in the subsequent nonlinear simulations. Each actuation reveals unique near-field vortical and acoustic responses that have a profound impact on far-field noise levels. The M0 actuation induces circumferentially interconnected strong streamwise vortices, while M1 actuation enhances the circumferential variability in the coherent structures. The M2 actuation encompasses both these effects, and along with a very low tonal impact of forcing, produces the most desirable far-field noise mitigation ( ${\sim }2.6\,{\rm dB}$ ), contributed by a broadband reduction around the column-mode peak of the baseline jet. Beyond M2 actuation, effectiveness of control saturates, particularly along the direction of peak noise radiation. Through a near-field analysis of the acoustic component, the efficacy of M2 actuation is attributed to the attenuation of the radiative efficiency of the jet, including reduced energy in the supersonic phase speeds, and redistribution of energy into the higher helical modes. Further, it curtails the nonlinear difference interactions in the plume that energize column-mode frequencies, which often appear as strong intermittent sound-producing events. While the shear layer turbulent kinetic energy decreases with actuation, the controlled jets show minimal variations in mean flow properties, particularly under M2 actuation, suggesting this to be a promising small-perturbation-based noise control strategy.

Research on diffusion characteristics of liquid jet effected by shock wave in supersonic high-enthalpy crossflow

The diffusion characteristics of liquid jets with phase transition under the action of shock waves in supersonic high-enthalpy crossflow were discussed in this paper. Numerous numerical simulations were carried out in high enthalpy inflow (Tt = 1680 K) under different shock wave intensity and injection parameter conditions. The Euler-Lagrangian method was employed to solve the gas-liquid two-phase flow coupling, and the evaporation, diffusion and mixing processes of kerosene were obtained. By analyzing simulation results, the influence and the mechanism of shock waves on enhanced kerosene mixing were revealed. The results show that increasing the shock wave intensity effectively improves the penetration and mixing of kerosene in general by changing the flow state and evaporation process. The penetration depth can be increased by up to 63.54 % in this paper. To balance the contradiction between total pressure loss and mixing efficiency, it is necessary to select an appropriate shock wave intensity. The enhanced diffusion and mixing process of kerosene by shock waves are related to the injection momentum ratio, evaporation momentum ratio and streamwise vortex intensity. Weakening mainstream momentum while boosting evaporation and vortex intensity effectively strengthens kerosene diffusion and mixing. This research significantly contributes to enhancing the diffusion and mixing of liquid kerosene and improving combustor performance.

Analysis of Near-wall Coherent Structure of Spiral Flow in Circular Pipe Based on Large Eddy Simulation

Based on the large eddy simulation method, this study performed the three-dimensional transient numerical analysis of the near-wall flow field of the spiral flow in a circular pipe and applied the sub-grid model of the kinetic energy transport. The low-speed bands, streamwise vortices and hairpin vortices of the spiral flow in the near-wall region of the circular pipe are determined using the Q criterion. The ejection and sweeping of coherent structures are identified using the velocity vector of the near-wall region; moreover, the two methods of creating the hairpin vortices are established by the image time series. The results demonstrate that the development directions of the near-wall bands, streamwise vortices and hairpin vortices of the spiral flow in the circular pipe develop along the path of the spiral line. The average spanwise period of the low-speed bands in the near-wall region is approximately 120 wall units, the length is more than 900 wall units and the height is not more than 40 wall units. The separation distance of the streamwise vortices is about 119 wall units. It has a certain angle with the wall (approximately 22°). The average burst period of a hairpin vortices is less than 0.015 s.

On the evolution of flow structures around a track cyclist

In this study, flow structures and their evolution over a track cyclist were investigated through wind tunnel tests. In supplement to the experiment, high-fidelity numerical simulations were also conducted to demonstrate the origins of global flow structures. In wind tunnel tests, a full-scale track cyclist mannequin was built based on the three-dimensional scanning of an elite track cyclist in a riding position of a sprint event, and a Cobra probe was used to measure the wake structures. The results show that the preeminent flow structures around the track cyclist mannequin are the streamwise vortices originating from different body parts. The evolution of these vortices involves strong vortex interactions and performs differently on each side, resulting in a dominant streamwise vortex merged behind the right thigh, which is associated with aerodynamic drag productions. In particular, leg position affects the lateral displacement between the elbow vortex and upper thigh, which is the reason for the distinct flow behaviors on each side. This study helps to better understand the flow around a track cyclist, facilitating the development of drag-saving strategies in the future.

Pulverized coal combustion in boundary layer turbulence using direct numerical simulation

The present study investigates pulverized coal combustion under oxy-fuel conditions interacting with turbulent boundary layer flows over a flat plate using direct numerical simulation (DNS). The coal particles are tracked in the Lagrangian framework while the flow is solved in an Eulerian way. Three cases with reacting particles, inert particles and single-phase flows were performed. The interplay between pulverized coal combustion, turbulent boundary layer flows and the wall was examined. It was shown that the coal particles first ignite in the outer layer of the boundary layer turbulence, where individual coal particle ignition occurs. The wall-normal velocity in the reacting case is larger compared with that of the non-reacting cases due to flow acceleration induced by combustion. The volatile matter mass fraction is high in the inner layer in the downstream region. However, the heat release rate is low due to the cold wall effect. The strong correlation between the wall heat flux and streak structures in the near-wall region is observed in all cases. The values of radiative heat transfer are similar in the upstream region of both the cases with reacting and inert particles. However, as combustion occurs and particle temperature increases in the reacting case, the radiative heat transfer from particles to the wall increases significantly in the downstream region. Particle accumulation due to turbophoresis in the near-wall region is analyzed. It was shown that the magnitude of streamwise vorticity is attenuated by coal combustion. Therefore, particle wall-accumulation is less prominent in the reacting case compared with the inert case.

Computational analysis of the fluid–structure interactions of a synthetic badminton shuttlecock

Fluid–structure interactions of a synthetic badminton shuttlecock at various flight speeds are investigated computationally. The cork of the shuttlecock is held fixed and its skirt is free to deform. The cross-sectional area of the skirt decreases with an increase in flight speed leading to a significant reduction in the drag compared to that for an undeformed shuttlecock. Four regimes of deformation, with an increase in speed, are identified. The deformation is steady and axisymmetric in regime 1. Beyond a certain speed, which is referred to as “buckling speed,” the deformation is in regime 2. The skirt assumes a non-axisymmetric shape with a significant increase in its rate of deformation with speed. It undergoes vibration in regime 3. The amplitude of vibration increases with increased speed. In regime 4, the vibrations are modulated atop a lower frequency wave that travels circumferentially along the skirt. Compared to a rigid shuttlecock at the same flow speed, the streamwise vortex structures inside the skirt are weaker in a deformed shuttlecock. The decrease in the drag coefficient with an increase in speed is due to a decrease in the cross-sectional area of the skirt as well as a reduction in the entrainment of the flow through the gaps in the skirt area. The computational results are in good agreement with the available experimental measurements. The effect of the elastic modulus of the material and various structural reinforcements is studied.