Rear Stagnation Point Research Articles

Transverse vortex-induced vibration of a sphere with the application of Lorentz force at low Reynolds number

In this study, the transverse vortex-induced vibration (VIV) of an elastically mounted sphere with the application of a streamwise Lorentz force is investigated through direct numerical simulation. The research parameter range is 300 ≤ Re ≤ 1100 and −0.8 ≤ N ≤ 1, where Re is the Reynolds number and N is the interaction parameter of the Lorentz force. The dependence of sphere responses, forces, and wake structures on Re and N is illustrated in detail. Within this range, two oscillation patterns are identified: VIV and desynchronization. Three wake patterns are identified: two-sided hairpin vortex emerges in the VIV region, while one-sided hairpin vortex and double-threaded wake structures are observed in the desynchronization region. The evolution of these wake patterns is related to the motion of the rear stagnation point (RSP) and separation line (SL) on the sphere surface. A large positive or negative Lorentz force suppresses the motion of RSP and SL, leading to the one-sided hairpin vortex or double-threaded wake structures replacing the two-sided hairpin vortex. Finally, the oscillation patterns are summarized on a map of amplitude response contours in the Re-N space.

An experimental study of a quasi-impulsive backwards wave force associated with the secondary load cycle on a vertical cylinder

Steep wave breaking on a vertical cylinder (a typical foundation supporting offshore wind turbines) will induce slam loads. Many questions on the important violent wave loading and the associated secondary load cycle remain unanswered. We use laboratory experiments with unidirectional waves to investigate the fluid loading on vertical cylinders. We use a novel three-phase decomposition approach that allows us to separate different types of nonlinearity. Our findings reveal the existence of an additional quasi-impulsive loading component that is associated with the secondary load cycle and occurs in the backwards direction against that of the incoming waves. This quasi-impulsive force occurs at the end of the secondary load cycle and close to the passage of the downward zero-crossing point of the undisturbed wave. Wavelet analysis showed that the impulsive force exhibits superficially similar behaviour to a typical wave-slamming event but in the reverse direction. To monitor the scattered wave field and extract run-up on the cylinder, we installed a four-camera synchronised video system and found a strong temporal correlation between the arrival time of the Type-II scattered wave onto the cylinder and the occurrence of this quasi-impulsive force. The temporal characteristics of this quasi-impulsive force can be approximated by the Goda wave impact model, taking the collision of the Type-II scattered waves at the rear stagnation point as the impact source.

Genetically-Based Active Flow Control And PIV Measurements Of A Circular Cylinder Wake

In the field of flow manipulation, considerable attention is devoted to controlling the wake of bluff bodies, which are characterized by the phenomenon of vortex shedding. Specifically, the control of the wake behind a single circular cylinder has garnered substantial research interest due to its engineering applications, such as reducing aerodynamic drag in the automotive and aerospace industries. Therefore, in the current work, through the application of the planar PIV technique, the fluid dynamic behavior of a circular cylinder wake controlled via synthetic jets (SJ) and Machine Learning (ML) methods is analyzed and discussed. ML algorithms are used to determine the optimal voltage signal for the loudspeaker, which effectively minimizes the aerodynamic drag of the cylinder. This approach overcomes the limitations associated with the a priori assumption of a parametric waveshape. In particular, the gradient-enriched machine learning control (gMLC) algorithm is chosen as optimization tool to search the best open-loop control policy for aerodynamic drag reduction. The cost function for this problem has been defined considering both the drag reduction contribution and the electrical power spent for the actuation. Initial optimization tests are performed by minimizing a cost function considering only the reduction in aerodynamic drag. Subsequently, a term related to the electrical power consumption for actuation is incorporated into the cost function. Once obtained the optimal control policies for these cases (hereinafter renamed CC1 and CC2, respectively), the physical mechanism responsible for reducing the aerodynamic drag is investigated more closely by analyzing the effect of the control laws on the turbulent flow statistics. Figure 1 reports a comparative assessment of the CC1 and CC2 with the baseline configuration and the configuration controlled by a sinusoidal law (CCS). The baseline configuration is characterized by an extended region of localized turbulent fluctuations in the far wake, where the time-averaged signature of von Kármán vortices is found. In contrast, all the controlled configurations show a global reduction in wake turbulence, with a peak of turbulent energy at the rear stagnation point due to the momentum injection from the SJ actuator. Notably, the CCS and CC2 configurations share similar flow field morphologies, while the CC1 configuration shows a greater reduction in turbulent fluctuations compared to the other controlled cases. This control law also achieves the largest drag reduction among all configurations studied reporting a 9.7% of drag reduction, compared to CCS and CC2, which exhibit similar reductions of 8.4% and 8.5%, respectively. Therefore, the optimization procedure has proven the capability of finding control policies able to outperform the traditional sinusoidal control widely studied in literature.

Large-scale flow field super-resolution via local-global fusion convolutional neural networks

Particle image velocimetry (PIV) techniques have a limited field of view of the flow field and can only capture high-resolution flow fields in localized areas. To obtain a larger measurement range, multiple cameras must be used to capture the flow field simultaneously and then stitch the parts together. However, this method can be expensive. We propose the local-global fusion convolutional neural network (LGF-CNN) for reconstructing large-field flow fields with high spatial resolution based only on two flow data types: local small-field high spatial resolution wake velocity fields and global large-field low spatial resolution velocity fields. The core of the model consists of convolutional neural network (CNN) architecture to learn the mapping relationship between the small field of view with high spatial resolution and the large field of view with low spatial resolution. Using the effectively trained LGF-CNN model, we demonstrate its ability to reconstruct high-resolution velocity fields around the circular cylinder. The LGF-CNN is rigorously validated on a number of representative datasets, including simulated data for Reynolds numbers of 200 and 500, as well as experimental data for a Reynolds number of 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. The results demonstrate the ability of LGF-CNN to generate accurate velocity fields with high spatial resolution, including reliable detection of high-frequency components. The proposed method could reduce the number of cameras required for large-field, high spatial resolution PIV measurements, thereby reducing experimental costs.

Thermal Radiation Effect on Unsteady MHD Rear Stagnation Point in Al2O3-Cu/H2O Hybrid Nanofluids

Thermal Radiation Effect on Unsteady MHD Rear Stagnation Point in Al2O3-Cu/H2O Hybrid Nanofluids

Stability Analysis of Unsteady Flow and Heat Transfer of Rear Stagnation Point in Hybrid Nanofluids with Thermal Radiation and Magnetic Impact

Stability Analysis of Unsteady Flow and Heat Transfer of Rear Stagnation Point in Hybrid Nanofluids with Thermal Radiation and Magnetic Impact

COMPUTATIONAL ANALYSIS OF FLOW CHARACTERISTICS AROUND A TWIN-SPLINED CYLINDER WITHIN A 2-D CHANNEL

In the present research work, external flow-induced stresses on a circular cylinder with double-splined surfaces are investigated at a Reynolds number Re of 100. Opposite sides of the cylinder have splined surfaces. The splines are positioned between 0° and 90° from the cylinder's front and rear stagnation points. It is demonstrated that the spline on the cylinder's leading edge modifies the vortex dynamics and causes considerable changes in flow-induced forces. At Re = 100, when a spline is placed on a cylinder's surface, noticeable reduction is observed in the coefficients of lift and drag compared to a smooth cylinder. When the inclination angle is increased to a maximum of 60°, the stagnation point moves to the windward side. Additionally, the spline in the front and back side of the cylinder significantly strengthens the vortex flow. At inclinations of 90° and 0°, maximal and minimal vorticities are obtained. Furthermore, the present work's double-spline cylinder demonstrates the advantage of reduced drag over many previously reported bluff bodies.

Viscoplastic flow past a cylinder near a moving wall

The flow of kaolinite mixed with water at mass fractions ≤28.5% past a cylinder near a moving wall is numerically investigated. The fluid is a non-Newtonian yield stress one and modeled as a Bingham plastic fluid. Simulations are performed at Reynolds numbers of 100≤Re≤1000 and Bingham numbers of 6.3≤Bn≤1153.1, which correspond to generalized Reynolds numbers of 0.55≤Regen≤503.6. Effects of the wall with the gap ratio varied in the range of G/D=0.1 and G/D=9 on the flow structures and the drag and lift coefficients are analyzed. The flow regime spans from laminar steady without and with boundary layer separation (and with two static unyielded zones formed at the front and rear stagnation points) to unsteady with periodic shedding of vortices behind the cylinder (and almost no unyielded zones in the near field). At small gaps, i.e., G/D≤1, both the drag and lift coefficients increase rapidly as the gap is decreased. They also increase with decreasing Regen. At G/D=9, influence of the wall is negligible, three approximations of the drag coefficient as a function of Regen are proposed.

The deformation and dynamics of a flexible plate with attached mass blocks mounted behind a circular cylinder

This paper presents a wind tunnel experiment on the deformation and dynamics of a flexible plate with attached mass blocks mounted behind a circular cylinder. The mass blocks are fixed at a distance of 3/4 of the plate length from the rear stagnation point of the cylinder. Different flexible plates with lengths ranging from 1D to 7D and thicknesses equaling 0.5%D and 1%D (where D is the cylinder diameter) are tested and compared. It is found that as the plate length increases, the deformation behavior of the flexible plate can be classified into three sequential regimes — “linear-shaped”, “fish-shaped”, and “trumpet-shaped” — with the Strouhal number decreasing gradually. The deformation regime changes at a longer plate length for the thicker flexible plate (1%D) than for the thinner one (0.5%D). Proper orthogonal decomposition (POD) analysis reveals that the deformation of the flexible plate is mainly dominated by the first two POD modes, and that the “fish-shaped” and “trumpet-shaped” regimes are characterized by the bending mode and deflection mode, respectively. Additionally, in the “trumpet-shaped” regime, the flexible plates have higher maximum and mean elastic strain energies. A kinematic analysis of the characteristic points on the flexible plate shows that the movement of the plate’s free end lags behind that of the mass blocks, and its phase lag decreases as the plate length increases. In particular, the fluctuating drag of the experimental model shows a step change when the deformation regime changes.

On the flow past ellipses in a Hele-Shaw cell

In this work we investigate the effect of vertical confinement and inertia on the flow past thin ellipses in a Hele-Shaw cell (with centre line velocity $U_c$ and height 2 $h$ ) with different aspect ratios for symmetrical flows and at an angle of attack, using asymptotic methods and numerical simulations. A Stokes region is identified at the ellipse vertices which results in flow different to flow past bluff bodies. Comparison with asymptotic analysis indicates close agreement over the ‘flat’ portion of the ellipse, for $\delta =(b/a)=0.05$ , where $a$ and $b$ are the semi-major and -minor ellipse axes, respectively. Two flow conditions are investigated for ellipses at an angle of attack of 10 $^\circ$ for a fixed $\delta =0.05$ . Firstly, for $\varLambda =(U_ca/\nu )(h/a)^2 \ll 1$ , the effect of increasing the vertical confinement of the Hele-Shaw cell results in the rear stagnation point (RSP) moving from close to the potential-flow prediction when $\epsilon =h/a$ is very small to the two-dimensional Stokes-flow prediction when $\epsilon$ is large. Secondly, for a fixed $\epsilon \ll 1$ , when inertia is increased past $\varLambda ={O}(\epsilon )$ the RSP moves towards the trailing edge and is located there for $\varLambda ={O}(1)$ . Under these conditions an attached exponentially decaying shear layer or ‘viscous tail’ is formed. A modified Bernoulli equation of the depth-averaged flow, together with the Kutta–Joukowski theorem is used to predict the drag and lift coefficients on the ellipse, which include a linear and a nonlinear contribution, corresponding to a Hele-Shaw and circulation component, respectively. Close agreement is found up to $\varLambda ={O}(1)$ .

Suppression of vortex-induced vibration of an elastically mounted sphere by electromagnetic force

In this paper, electromagnetic force on two degrees of freedom vortex-induced vibration (VIV) of an elastically mounted sphere for vibration suppression is numerically achieved at Re = 300. The relations between the wake structures, velocity and pressure distributions, force coefficients, and sphere displacement are investigated by varying the interaction parameter (N) of electromagnetic force. With the increase in N, the momentum of the fluid near the sphere is enhanced to control the flow separation. Therefore, both the rotation radii of the rear stagnation point (RSP) and the separation line (SL) decrease, causing the spiral vortices to become thinner. This leads to a reduction in the fluctuation amplitude of the lift coefficient and mitigates the VIV. As N exceeds 0.5, the periodic spiral vortices transform into a steady double-thread wake due to the stopping of RSP and SL rotation. Therefore, a constant lift is generated in the z-direction due to the asymmetric flow field in the x–z plane, which is accompanied by the VIV fully suppressed. Moreover, the effect of electromagnetic locations (θm) on vibration suppression is examined. With the increase of θm, the vibration suppression efficiency increases first and then decreases, which achieves the maximum vibration suppression efficiency at θm = 125°. The reason is that the electromagnetic force covers the location of the half-circle-shaped SL, which has a significant effect on the control of the flow separation.

Pressure Fluctuations in the Base of a Typical Re-Entry Module

Unsteady pressure measurements were carried out on the flow side and around the base of a blunt-nosed bluff body representing a spacecraft re-entry module in the Mach number range of 0.8 to 4.0. The results show that the pressure fluctuations in the base region are much higher than in the attached flow region of the body. Most of the energy in the pressure fluctuations in the base region is in the low-frequency band, while fluctuations in the attached flow region occur over a wider bandwidth. In the separated flow region at the base, highest pressure fluctuations were observed around the rear stagnation point. The frequency spectra do not show any dominant tone attributable to the configuration at any measurement location. The observations suggest that vortex shedding behind such 3-d bluff bodies could be relatively weak and that most of the fluctuating energy in the separated flow region could be due to random oscillations of the rear stagnation point.

Three-dimensional numerical investigation of a transversely oscillating slotted cylinder and its applications in energy harvesting

The present paper numerically investigates the fluid dynamics associated with the flow over an elastically mounted circular cylinder at a Reynolds number of 500. A slit normal to the flow direction is placed at the cylinder's centre. The study covers the large parametric set of calculations for the combined mass-damping ratio $m^{*}\zeta = 0.2$ , including the slit offset for six different offset angles ( $-30^\circ \leq \alpha \leq +30^\circ$ ) measured from the vertical axis at the centre point of the cylinder and the effect of slit widths ( $0.1 \leq s/D \leq 0.3$ ) on the aerodynamic loading, vibration response and associated flow characteristics. Furthermore, a wide range of reduced velocities ( $3\leq U_r \leq 7$ ) are examined for the complete closure of studying the effect on the vortex-induced vibration response. The results demonstrate that adding the normal slit increases the periodic suction-blowing phenomena, strengthening the vortex shedding. The results suggest that the normal slit can suppress or increase vortex-induced vibration depending on the slit-offset angle. Placing it toward the front stagnation point results in the increased oscillation amplitude (with a wider wake behind the cylinder) while shifting it toward the rear stagnation point diminishes the cylinder's oscillations. The paper reveals that this dual behaviour of the normal slit (based on its offset placement) is closely related to the phase difference between the lift force and the oscillation amplitude. Various vortex-shedding patterns associated with the different slit-offset angles are duly reported in the paper. Furthermore, a magnet is attached to the slit cylinder, and its effect on the energy harvesting capability via a coil-magnet arrangement is explored in detail for a wide range of reduced velocities.

The transformation mechanisms of vortex structures on vortex-induced vibration of an elastically mounted sphere by Lorentz force

The transformation mechanisms of vortex structures on vortex-induced vibration (VIV) of an elastically mounted sphere by Lorentz force are numerically investigated at Re = 300. The relations among the sphere trajectories, wake structures, vorticity distribution, and the rotation characteristics of the rear stagnation point (RSP) and separation line (SL) are discussed before and after the application of Lorentz force. From this, the transformation mechanisms of vortex structures on sphere VIV are revealed. The sphere, when released, initially begins to vibrate along a linear path in the transverse plane and then transforms smoothly into a circular path, which leads to the transition from hairpin vortices to spiral vortices. After the application of Lorentz force, the fluid near the sphere is accelerated. The rotations of the RSP and SL are fully suppressed, which leads to the transition from the spiral vortices to the double-thread wake. Moreover, the wake structures vary with the interaction parameter N of the Lorentz force. The spiral vortices arise for small values of N, where the vibration magnitude grows for N = -0.2 and decays for N = 0.2. When N is increased to 1, the vibration of the sphere is fully suppressed. Therefore, the spiral vortices are replaced by the steady double-thread wake.

Drag Reduction for Flow Past Circular Cylinder Using Static Extended Trailing Edge

AbstractA numerical study has been carried out on the two-dimensional flow past a circular cylinder. In this case, a splitter plate is provided at the rear stagnation point in the downstream direction. ansys fluent has been used to carry out the numerical simulations based on finite volume method approach. Grid independence was achieved and the numerical model was validated with results available in open literature at Reynolds numbers of 100, 5000, and 100,000 respectively. In the present investigation, the characteristics of vortex shedding due to the presence of splitter plate in the circular cylinder were investigated. The main focus of this research was to find the optimal splitter plate length for low, moderate, and high Reynolds numbers. It was observed that at low, moderate, and high Reynolds numbers, the drag coefficient (cd) for optimal plate length decreased drastically as compared to the baseline circular cylinder case. Moreover, the fluctuating nature of lift coefficient (cl) had also ceased. This research work has a good potential to decrease time-varying structural loads on bluff bodies by decreasing the vortex shedding frequency and consequently decreasing drag. The scope of our research extends to structures of bridges and large vehicles, radiator pipes of heat exchangers, landing gears of aircraft, and many more.

DeepTRNet: Time-resolved reconstruction of flow around a circular cylinder via spatiotemporal deep neural networks

We propose spatiotemporal deep neural networks for the time-resolved reconstruction of the velocity field around a circular cylinder (DeepTRNet) based only on two flow data types: the non-time-resolved wake velocity field and sparse time-resolved velocity measurements at specific discrete points. The DeepTRNet consists of two operations, i.e., compact spatial representations extraction and sequential learning. We use the convolutional autoencoder (CAE) in DeepTRNet to extract compact spatial representations embedded in the non-time-resolved velocity field. The nonlinear CAE modes and corresponding CAE coefficients are thus obtained. Based on the nonlinear correlation analysis of the velocity field, we use the bidirectional recurrent neural networks (RNN) with the gated recurrent unit for mapping the sparse time-resolved velocity measurements to the CAE coefficients via sequential learning. The early stopping technique is used to train the DeepTRNet to avoid overfitting. With the well-trained DeepTRNet, we can reconstruct the time-resolved velocity field around the circular cylinder. The DeepTRNet is verified on the simulated datasets at two representative Reynolds numbers, 200 and 500, and the experimental dataset at Reynolds number 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. We systematically compare the DeepTRNet method and the RNN-proper orthogonal decomposition (POD) approach. The DeepTRNet can obtain the accurate time-resolved velocity field depending on the two data types mentioned above. The DeepTRNet method outperforms the RNN-POD method in the reconstruction accuracy, especially for the reconstruction of small-scale flow structures. In addition, we get the reliable velocity field even for the high-frequency components.

Correspondence between the number of no-slip critical points and nature of rear stagnation point of a symmetric object

For flow around an isolated object, the points of zero vorticity/shear stress located at fluid–solid interface, i.e., the separation, reattachment points inclusive of forward and rear stagnation points are refered to as no-slip critical points. The total number, n (≥2), of such points is an even number. For flow past a diamond-section object, it is shown here that a change of the value of n by 2 alters the nature of its rear stagnation point. The rear stagnation point acts as a separation point for n = 2, 6, 10, etc. and as an attachment point for n = 4, 8, 12, etc. A pair of hypothetical mean wakes is proposed and their viability discussed with reference to results available in literature. Concerning flow past two in-line diamond cylinders, the formation of an “anti-wake” at the leading edge of the downstream cylinder renders its forward stagnation point to act as a separation point, which, otherwise for an isolated object, invariably serves as an attachment point. The forebody and afterbody of a symmetric object act as independent entities in influencing the nature of no-slip stagnation points.

Ignition studies of hydrogen-air mixtures over hot wire

Hot surface ignition of combustible gas mixtures poses a safety threat in many engineering applications. Gaseous mixtures ignite when hot surface temperature reaches the ignition threshold. In the present work, two-dimensional numerical simulations with detailed reaction mechanism are performed to simulate the flow of stoichiometric hydrogen-air mixture over a stationary hot wire. The effect of heating rates, wire diameters, mixture inlet velocities, and mixture equivalence ratios on the ignition threshold is investigated. In all the cases investigated, ignition is found to occur at the rear stagnation point, and wire heating rate did not influence the ignition phenomenon significantly. With an increase in mixture inlet velocity and mixture equivalence ratio, the ignition threshold increases, whereas the threshold has been found to decrease with increasing wire diameters. The role of the local equivalence ratios at the ignition point and reaction rates prior to the ignition process has been studied to help better understand the ignition phenomenon under different conditions.

Combined effect of bending stiffness and streamwise length of the attached flexible splitter plate on the vortex-induced vibration of a circular cylinder

A flexible splitter plate attached to the rear stagnation point of a circular cylinder is applied to control the vortex-induced vibration. The influence of its bending stiffness on the control effect is experimentally investigated for two streamwise lengths of 1D and 2D (D is the cylinder diameter). Five dimensionless bending stiffnesses are selected: 0.979 (P1), 3.123 (P2), 6.797 (P3), 23.087 (P4), and 47.484 (P5). The characteristics of cylinder vibration, flow field, lift, and plate dynamics are synchronously studied. The results show that the effect of the bending stiffness depends on the streamwise length of the plate. For the flexible splitter plate of 1D, the best suppression effect of cylinder vibration is achieved for the P2 case, where maximum vibration amplitude is reduced by 93%, while the galloping-like vibration is excited for P4 and P5 cases. According to the analysis of the plate dynamics and the wake development, a large plate vibration is expected to suppress the galloping-like vibration. The bending stiffness affects the vibration state of the flexible splitter plate, and consequently, the wake vortex development and dynamic response of the cylinder are changed. For the flexible splitter plate of 2D, the vibration amplitude response of the cylinder can be divided into three categories based on the variation of amplitude versus the reduced velocity. For P2-P5 cases, a beneficial phenomenon that a frequency branch is larger than the natural frequency occurs.

Drag Reduction on a Three Dimensional Teardrop-Shaped Body Car with Different Stagnation Points

The long-term goal in the automotive industry is to reduce fuel consumption and environmental pollution without compromising the aerodynamic performance of the car. Herein, the aerodynamic performance of an in-house designed Shell Eco-Marathon prototype car is analyzed using Computational Fluid Dynamics simulations. Shape optimization of the Shell car is executed to reduce drag by modifying the rear underbody profile and stagnation point position. The effect of one modification to another is studied to determine the changes to overall flow around the car and, more importantly, the lift and drag coefficients. It has been found that the stagnation point height has a higher influence on the aerodynamic performance of the car compared to variations of the rear underbody, with optimum drag reductions of 17% and 10%, respectively. Moreover, combining the two best configurations to the car reduces CD by 25%, and this marks the highest drag reduction achieved in this study.