Unsteady Vortex Shedding Research Articles

Bistable states in the wake of a wavy cylinder

Wavy cylinders have been recognized as a type of effective flow control device in previous studies. In this paper, we investigate the wake dynamics of an optimally designed wavy cylinder that completely suppresses the Kármán vortex shedding. Such a wavy cylinder is forced to oscillate with a sinusoidal motion in the crossflow direction. Examination of the lift force spectrum reveals that for a fixed forcing amplitude, a critical forcing frequency exists, below which the flow control effectiveness of the wavy cylinder is retained and beyond which the inherent vortex shedding resurrects. The resurrected unsteady vortex shedding can persist even without sustained forcing. This indicates that in addition to the steady state developed from uniform initial condition, an oscillatory state exists in the wake of a wavy cylinder if the initial state is sufficiently perturbed. The newly revealed unsteady flow features comparable hydrodynamic performance with the benchmark two-dimensional cylinder. The discovery of the bistable states calls for re-examination of the flow control effectiveness of the wavy cylinder in more complicated inflow conditions.

Vortex shedding characteristics in the wake of circular finned cylinders

The near wake flow development and vortex shedding characteristics downstream of straight circular finned cylinders are experimentally investigated. Different finned cylinders with the same fin pitch and fin thickness, but different diameter ratios, Df/Dr = 1.5, 2.0, 2.5, are investigated. Particle image velocimetry measurements are carried out at a Reynolds number of Re = 2.0 × 104 based on the cylinder effective diameter (Deff), which corresponds to the sub-critical flow regime. The spatial flow development in the near wake is elucidated using both time-averaged and phase-resolved flow field characteristics. The proper orthogonal decomposition analysis is used to characterize the unsteady vortex shedding process in the wake of the cylinders. The results show that adding fins to the cylinder changes the flow development around it. Moreover, the extent of the recirculation region reduces significantly downstream of the finned cylinders as their diameter ratio increases due to higher flow entrainment between the fins. This causes an increase in both the energy of the primary vortex shedding and the strength of the vortices in the wake. The combination of stronger vortices with amplified periodicity leads to a more energetic vortex shedding process in the wake of the finned cylinders.

Wake structure of laminar flow past a sphere under the influence of a transverse magnetic field

The wake structure of an incompressible, conducting, viscous fluid past an electrically insulating sphere affected by a transverse magnetic field is investigated numerically over flow regimes including steady and unsteady laminar flows at Reynolds numbers up to 300. For a steady axisymmetric flow affected by a transverse magnetic field, the wake structure is deemed to be a double plane symmetric state. For a periodic flow, unsteady vortex shedding is first suppressed and transitions to a steady plane symmetric state and then to a double plane symmetric pattern. Wake structures in the range $210<Re\leqslant 300$ without a magnetic field have a symmetry plane. An angle $\unicode[STIX]{x1D703}$ exists between the orientation of this symmetry plane and the imposed transverse magnetic field. For a given transverse magnetic field, the final wake structure is found to be independent of the initial flow configuration with a different angle $\unicode[STIX]{x1D703}$. However, the orientation of the symmetry plane tends to be perpendicular to the magnetic field, which implies that the transverse magnetic field can control the orientation of the wake structure of a free-moving sphere and change the direction of its horizontal motion by a field–wake–trajectory control mechanism. An interesting ‘reversion phenomenon’ is found, where the wake structure of the sphere at a higher Reynolds number and a certain magnetic interaction parameter ($N$) corresponds to a lower Reynolds number with a lower $N$ value. Furthermore, the drag coefficient is proportional to $N^{2/3}$ for weak magnetic fields or to $N^{1/2}$ for strong magnetic fields, where the threshold value between these two regimes is approximately $N=4$.

A boundary thickening-based direct forcing immersed boundary method for fully resolved simulation of particle-laden flows

A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the local communications between the Lagrangian points on the solid boundary and their neighboring fluid Eulerian grids are improved, based on an implicit direct forcing (IDF) approach and a partition-of-unity condition for the regularized delta function. This strategy yields a simple, yet much better imposition of the non-slip and non-penetration boundary conditions than the conventional direct forcing (DF) technique. In particular, the present BTDF method can achieve a numerical accuracy comparable with other representative improved methods, such as multi-direct forcing (MDF), implicit velocity correction (IVC) and the reproducing kernel particle method (RKPM), while its computing cost remains much lower than them and nearly equivalent to the conventional DF method. The dependence of the optimum thickness value of boundary thickening on the form of the different regularized delta functions is also revealed. By coupling the lattice Boltzmann method (LBM) with BTDF-IB, the robustness of the present BTDF IB method is demonstrated using numerical simulations of creeping flow (Re=0.1), steady vortex separating flow (Re=40) and unsteady vortex shedding flow (Re=200) around a circular cylinder. The accuracy and robustness of the present method for moving particle-laden flows are performed on three benchmark cases, such as free sedimentation of single circular cylinder, DKT sedimentation of two particles and Rayleigh-Taylor instability of 504 particles sedimentation in an enclosed cavity. The computational efficiency between the present BTDF method and the MDF method is also compared at last.

Application of variable-time-period harmonic balance method to periodic unsteady vortex shedding

The harmonic balance method (HBM) is an efficient frequency-domain approach to computing periodically unsteady flows. The basic principle of this method is to decompose the flow variables into a Fourier series, and transform the unsteady flow into several steady problems coupled by a spectral time-derivative operator, from which the whole time history of a complete unsteady periodic flow can be reconstructed. In the present work, we investigate the ability of the HBM to be used for modeling the periodic unsteady vortex shedding behind a bluff body at low Reynolds numbers via solving the unsteady incompressible Navier-Stokes equations. For the periodic problem where the time period <i>T</i> of the unsteadiness is unknown, a variable-time-period method based on residual gradients is used to compute the exact time period iteratively starting from an initial guess <i>T</i><sub>0</sub>. By simulating the two-dimensional laminar flows over a circular cylinder and a square cylinder, the accuracy and efficiency of the HBM are investigated and the effects of different parameters on the final results are analyzed. Comparisons with the results of fixed-time-period HBM using a constant time period are also implemented. Three practical methods of optimization are used to iterate the time period, and the values of accuracy and efficiency of different methods are compared with each other. The results show that the HBM can accurately capture the complex nonlinear flow field physics with only three harmonics. The Strouhal frequency and mean drag coefficient each as a function of the Reynolds number agree well with existing experimental and computational data. For both test cases, the computational efficiency of HBM is higher than that from the traditional time-domain method. For the square cylinder test case, the HBM offers speedup rate up to nearly 18 times. The real time period of vortex shedding can be predicted by the gradient based variable-time-period method, and the final result is insensitive to search step <i>λ</i>. The calculation result is sensitive to the initial <i>T</i><sub>0</sub>, and when such a variable is greater than a certain value, the result will converge to an approximate integer multiple of the real one. Therefore, it deserves further exploration on how to specify this initial condition. The shedding time periods computed by different optimization methods are converged to the same value. The computational efficiency from the FR conjugate gradient method and that from Newton method are both equivalent to that from the steepest descent method with the maximum search step <i>λ</i> = 100. Avoiding prescribing parameters such as the search step <i>λ</i>, the Newton method possesses higher application value in engineering calculation than the other two schemes.

Large Eddy Simulation of an asymmetric spinnaker

This work presents a numerical study into the aerodynamics of downwind sailing using different methods for modelling turbulence, comparing Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) methods. Previously published experimental data of downwind sails have shown areas of flow separation and vortex structures at the leading and trailing edge of the gennaker, making these sails challenging to model accurately. The ability of LES to model the transition to turbulence within separated shear layers can lead to an accurate prediction of the leading edge separation bubble, which significantly influences the flow field around the top half of the sail, and downstream of the layer's reattachment. The transient nature of the LES solution allows the computation of the creation and shedding of unsteady vortices at the leading edge and downstream of the sail draft. The effect of the vortex rolls being convected towards the trailing edge is to generate a boundary layer which is more resistant to separation. Comparison with the pressure distribution measured in experiment shows that LES correctly predicts the location of separation, while RANS erroneously predicts a larger region of stalled flow which limits the suction on the sail. As a result, the overall drive and side forces computed by the LES are in better agreement with the experimental data, with less than 3.5% error, that the RANS which underestimates their magnitude by more than 14%. However, it should be noted that the accuracy of the LES calculations has not been demonstrated, and so the results should be treated with caution and not considered conclusive.

Large-eddy simulation of flow over a rotating cylinder: the lift crisis at

We present wall-resolved large-eddy simulation (LES) of flow with free-stream velocity $\boldsymbol{U}_{\infty }$ over a cylinder of diameter $D$ rotating at constant angular velocity $\unicode[STIX]{x1D6FA}$ , with the focus on the lift crisis, which takes place at relatively high Reynolds number $Re_{D}=U_{\infty }D/\unicode[STIX]{x1D708}$ , where $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the fluid. Two sets of LES are performed within the ( $Re_{D}$ , $\unicode[STIX]{x1D6FC}$ )-plane with $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D6FA}D/(2U_{\infty })$ the dimensionless cylinder rotation speed. One set, at $Re_{D}=5000$ , is used as a reference flow and does not exhibit a lift crisis. Our main LES varies $\unicode[STIX]{x1D6FC}$ in $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 2.0$ at fixed $Re_{D}=6\times 10^{4}$ . For $\unicode[STIX]{x1D6FC}$ in the range $\unicode[STIX]{x1D6FC}=0.48{-}0.6$ we find a lift crisis. This range is in agreement with experiment although the LES shows a deeper local minimum in the lift coefficient than the measured value. Diagnostics that include instantaneous surface portraits of the surface skin-friction vector field $\boldsymbol{C}_{\boldsymbol{f}}$ , spanwise-averaged flow-streamline plots, and a statistical analysis of local, near-surface flow reversal show that, on the leeward-bottom cylinder surface, the flow experiences large-scale reorganization as $\unicode[STIX]{x1D6FC}$ increases through the lift crisis. At $\unicode[STIX]{x1D6FC}=0.48$ the primary-flow features comprise a shear layer separating from that side of the cylinder that moves with the free stream and a pattern of oscillatory but largely attached flow zones surrounded by scattered patches of local flow separation/reattachment on the lee and underside of the cylinder surface. Large-scale, unsteady vortex shedding is observed. At $\unicode[STIX]{x1D6FC}=0.6$ the flow has transitioned to a more ordered state where the small-scale separation/reattachment cells concentrate into a relatively narrow zone with largely attached flow elsewhere. This induces a low-pressure region which produces a sudden decrease in lift and hence the lift crisis. Through this process, the boundary layer does not show classical turbulence behaviour. As $\unicode[STIX]{x1D6FC}$ is further increased at constant $Re_{D}$ , the localized separation zone dissipates with corresponding attached flow on most of the cylinder surface. The lift coefficient then resumes its increasing trend. A logarithmic region is found within the boundary layer at $\unicode[STIX]{x1D6FC}=1.0$ .

Study on flapping modes of a flexible filament in the wake of an upstream rotating cylinder

Flapping mode of a flexible filament in wake flow behind a rotating circular cylinder has been studied numerically by using of an immersed-boundary-based lattice Boltzmann method. In a parameter space of α =0.1–3.0 and G /D=0.05–3.5, where α is the cylinder rotation rate and G / D is the distance ratio between the filament and cylinder which has a diameter of D , flapping modes of the filament are analyzed in the phase diagram to examine the mode transition features and the mechanism of formation for different modes. Specifically, three kinds of flapping modes have been found which are labelled as reversed, coiled, and normal flapping modes; six sub-modes: reversed one-side, two-side and steady modes, and normal one-side, two-side and steady modes have been identified. Based on the phase diagram in the ( α , G /D) plane, the transition pathways from the reversed to normal modes have been revealed as a consequence of increasing G / D . The critical value of G / D for transitions to the normal flapping modes demonstrates a decreasing trend for a small rotation rate, then becomes unaltered for a large α . The forming mechanism of different modes has been explored by analyzing the vortical wake behind the rotating cylinder and flexible filament. Moreover, great feedback effect of filament flapping on the cylinder wake flow has been revealed. Specifically, at specific parameters, the interaction between the flapping filament and the cylinder wake flow acts to totally suppress or trigger on the unsteady vortex shedding behind the cylinder, which correspondingly leads to great drag reduction even generation of thrust for the rotating cylinder, or significant drag enhancement.

UNSTEADY CHARACTERISTICS OF THE SHOCK PROPAGATION IN A CONVERGENT SHOCK TUBE WITH SMALL ANGLE

The whole evolution of the incident shock propagation in a convergent shock tube with small angle is studied in detail by using the direct numerical simulation. Specifically, the shape of the curved shock and the unsteady flow patterns which differs from the K-H instability, have been evaluated. The results show that as a disturbance of the inclined wall on the shock, the bending position of the incident shock represents periodically changed and its non-dimensional wavelength is larger when the convergent angle becomes greater, indicating a faster response to the curvature variation. At the same time, two different flow instable patterns for the shock propagation in the area reduction channel are discovered, one of which is the asymmetric shock bifurcations when the reflected shock from the collision of the right wall interacts with the boundary layer. This instability is closely related to the unsteady vortex shedding behind the bifurcated feet, resulting in the dramatic pressure fluctuation. Another pattern occurs when the reflected shocks generated by the curved incident shock impinge on the upper and lower walls. The collision position moves at a modest speed, which causes the formation of small vortices near the reflection regions. Article DOI: https://dx.doi.org/10.20319/mijst.2018.42.4662 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Reynolds number Re=40-200 and various rotation rate theta_i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method (FVM). The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re increases, the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution for theta_i <theta_crit. It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.

Ignition of combustible mixtures by hot particles at varying relative speeds

ABSTRACTDetailed numerical simulations have been performed to study the ignition behavior of hot spherical particles at atmospheric conditions. The particles move relative to a combustible gas with a velocity of 0–30 m s, which spans different flow regimes, from creeping flow to unsteady vortex shedding. The temperature of the particles’ surface increases linearly over time and is recorded at ignition for methane/air and hydrogen/air mixtures. For low relative velocities m s or Reynolds numbers , increases proportionally to or and the flow field is axisymmetric. For higher relative velocities, an unsteady vortex street forms behind the particle so that three-dimensional simulations are required. A correlation employing the van’t Hoff criterion yields linear correlations based on the Nusselt number and for both the low- and high-velocity ranges. For rich hydrogen flames at high velocities, the flame temporarily stabilizes near the hot particle in the recirculation zone downstream. As the surface temperature increases further, the flame suddenly starts to propagate downstream, leading to two distinct ignition events: local ignition at the particle’s surface and start of the propagation into the surrounding gas. The latter yields a much steeper increase of ignition temperature with incoming flow velocity.

Pitch and aspect ratio effects on single-phase heat transfer through microscale pin fin heat sinks

Heat transfer and pressure drop of single-phase liquid flow is characterized in eight micro pin fin heat sinks with varied pitch and aspect ratios. The pins are diamond shaped with respect to the flow and have transverse pitch-to-diameter (ST/Dh) and aspect (Hpin/Dh) ratio variations in the range of 1.7–3.0 and 0.7–3.2, respectively. The fluid used is PF-5060 over a Reynolds numbers (based on pin fin hydraulic diameter) range of 8–1189. Flow visualization is performed on all the heat sinks and flow transition into unsteady vortex shedding is observed only in those with specific pitch and aspect ratios. Flow visualization reveals upstream propagation of the onset of vortex shedding along the length of heat sink with an increase in Reynolds number. The existence of vortex shedding in micro pin fin heat sinks affects the prediction error of heat transfer correlations in literature. To address this gap, together with data from a prior study using liquid nitrogen [1], separate correlations are developed to predict Nu in the steady and unsteady regimes. The resulting correlation for the unsteady regime shows significantly decreased dependency of Nusselt on the Prandtl number compared to the non-vortex-shedding condition.

Optimal streaks in the wake of a blunt-based axisymmetric bluff body and their influence on vortex shedding

We compute the optimal perturbations of azimuthal wavenumber m THAT maximize the spatial energy growth in the wake of a blunt-based axisymmetric bluff body. Optimal perturbations with m≠0 lead to the amplification of streamwise streaks in the wake. When forced with finite amplitude m≠1, optimal perturbations have a stabilizing effect on large-scale unsteady vortex shedding in the wake. We show that m≥2 modes, which are forced with zero mass flux, can significantly reduce the amplitude of the unsteady lift force exerted on the body. When combined with low levels of base bleed, these perturbations can completely suppress the unsteadiness in the wake with reduced levels of mass injection in the flow.

Unsteady Flow Structures and Pressure Pulsations in a Nuclear Reactor Coolant Pump With Spherical Casing

Severe vibrations induced by flow instabilities in the nuclear reactor coolant pump (RCP) are detrimental to the safe operation of the pump. Due to the particular spherical casing in the RCP, the internal flow structures are extremely ambiguity and complicated. The goal of the present work is to shed comprehensive light on the unsteady flow structures and its correlation with the pressure pulsations by using large eddy simulation (LES) method of the RCP. The vorticity distribution and the shedding vortex from the blade trailing edge are depicted in detail. Furthermore, the internal correlations between the flow unsteadiness and pressure pulsation are illustrated in some special regions of the RCP. Evidently, some main excitation components in the pressure spectra are excited by the shedding vortex. Besides, components at blade passing frequency (fBPF) are closely associated with rotor–stator interaction between the wake flow from the impeller outlet and unsteadiness vortexes shedding from the diffuser blade trailing edge. It is thought to be that the pressure pulsations of the RCP are closely associated with the corresponding vorticity distribution and the unsteady vortex shedding effect.

Numerical simulation of flow characteristics behind the aerodynamic performances on an airfoil with leading edge protuberances

ABSTRACTThis article presents a numerical investigation of the effects of leading-edge protuberances on airfoil stall and post-stall performance. An improved delayed detached eddy simulation (IDDES) method was adopted. As a result, to clarify the effects of ‘bi-periodic’ phenomenon around stall region, it was found that the flow separation at troughs was the main inducement of aerodynamic lift degradation within pre-stall regime and the flow pattern where vortices diverged was predominant. It was also found that the variations in flow patterns led to the gentle stall process. Furthermore, to study the statistical characteristics of unsteady vortex shedding, corresponding spectrum characteristics were also analyzed from another perspective, suggesting that the vortex shedding frequency was higher where vortices converged. Eventually, the improved performances of tubercled airfoil within post-stall regime could be attributed to the strong streamwise vortices generated by the leading-edge protuberances. Deploying the methods of vortex dynamics, the generation and evolution of the streamwise vortices were depicted. It turned out that the primary and secondary vortices were induced by spanwise pressure gradient at airfoil surface; meanwhile, vortex stretching played a key role in primary vortex evolution, which initially enhanced the strength of vortices corresponding to the acceleration of streamwise velocity.

Regeneration of turbulent fluctuations in low-Froude-number flow over a sphere at a Reynolds number of 3700

Direct numerical simulations (DNS) are performed to study the behaviour of flow past a sphere in the regime of high stratification (low Froude number $Fr$). In contrast to previous results at lower Reynolds numbers, which suggest monotone suppression of turbulence with increasing stratification in flow past a sphere, it is found that, below a critical $Fr$, increasing the stratification induces unsteady vortical motion and turbulent fluctuations in the near wake. The near wake is quantified by computing the energy spectra, the turbulence energy equation, the partition of energy into horizontal and vertical components, and the buoyancy Reynolds number. These diagnostics show that the stabilizing effect of buoyancy changes flow over the sphere to flow around the sphere. This qualitative change in the flow leads to a new regime of unsteady vortex shedding in the horizontal planes and intensified horizontal shear which result in turbulence regeneration.

On the Unsteady Behavior of the Flow around NACA 0012 Airfoil with Steady External Conditions at Re=1000

Even for the stationary airfoils, due to the boundary and shear layer interactions of upper and lower surface of the airfoils, alternating vortex patterns form and the flow becomes time dependent. In the current study, the unsteady behavior of the flow around a symmetric airfoil is considered as incidence angle increases. The flow patterns are presented for wide range of angles of attack values. The vortex pattern generated is analyzed numerically for different angles of attack at Re=1000 around NACA 0012 airfoil. At this Reynolds number, the flow is laminar and boundary layers are quite thick. Flow separation and unsteady vortex shedding is observed even at low angles of attack. For NACA 0012 airfoil, the unsteady vortex pattern is observed at about 8° angle of attack for Re=1000. Spectral analysis is performed for angles of attack ranging from 0° to 90°. It is presented that amplitude spectrum of lift coefficient (C1) start to shows a peak at 8° for NACA 0012 and the aerodynamic forces presents oscillatory behavior afterwards. The effect of angle of attack to wake pattern and instantaneous and mean aerodynamic coefficients are discussed. The time-averaged streamlines, pressure and skin friction coefficients are analyzed to observe the vortex formation and separation from the airfoil upper surface at this low Reynolds number.

Impact of numerics on the predictive capabilities of reacting flow LES

Combustors in modern aerospace propulsion systems are highly optimized devices and further enhancements to their performance will require advanced predictive modeling techniques. The LES approach has potential to be such a technique, but demonstration of its true predictive capability remains a challenge. In this paper, a methodical study is performed to assess the impact of numerical error on the predictive capabilities of LES and to distinguish it from error arising from physical modeling. Four codes are employed to simulate the bluff body stabilized flame experiment of Volvo Flygmotor AB. The physical models (governing equations and sub-grid models) are kept identical between the codes so that the physical modeling error is the same. For the same reason, computational grids are also kept identical since the sub-grid models are grid dependent. Results indicate that all codes produce a very similar solution for the non-reacting flow in terms of large scale unsteady vortex shedding behavior, mean profiles and second order turbulence statistics, on a suitably refined grid. This solution is also very close to the experimentally observed behavior of the flow. In contrast, for the reacting case, solutions from the various codes exhibit significant differences when analyzed under the same metrics and with similar or even finer grid resolution than that used for the non-reacting case. These differences are large enough to change the macroscopic behavior of the flow, e.g. some codes predict symmetric vortex shedding while others predict asymmetric shedding and some codes show strong recirculation zones while others show stagnant regions behind the bluff body. It is also shown that none of the solutions truly predicts the experimentally observed flow. Given that the physical sub-grid models and computational grids are the same in all the simulations, the inconsistency between results points to a significant impact of numerical methods and, hence, numerical error. The need for mitigation of this impact is highlighted, along with the need for metrics detailing how LES should be applied to reacting flows. It is suggested that both of these issues should be the focus of future work.

Experimental study on the flow regimes past a confined prism undergoing self-sustained oscillations

An experimental study based on Particle Image Velocimetry (PIV) is presented with the objective of studying the flow regimes that appear in the flow past a confined prism undergoing self-sustained oscillations at low Reynolds numbers (Re). The square-section prism, placed inside a 3D square cross-section vertical channel with a confinement ratio of 1/2.5, was tethered to the channel walls and, therefore, it was allowed to move freely transverse to the incoming flow. Re (based on the prism cross-section height) was varied in the range from 100 to 700. Three different prism to fluid density ratios (m∗) were considered: 0.56, 0.70, and 0.91. These two parameters, Re and m∗, were used to map the results obtained. In particular, it was found that five different regimes appear: (1) steady prism with steady recirculation bubble, (2) steady prism with unsteady vortex shedding wake, (3) large amplitude low frequency oscillating prism with unsteady vortex shedding wake, (4) small amplitude high frequency oscillating prism with unsteady vortex shedding wake, and (5) irregular/chaotic motion of both the prism and the wake. The PIV results and associated numerical simulations were used to analyze the different prism and wake states.

Flow-excited acoustic resonance of a Helmholtz resonator: Discrete vortex model compared to experiments

The acoustic resonance in a Helmholtz resonator excited by a low Mach number grazing flow is studied theoretically. The nonlinear numerical model is established by coupling the vortical motion at the cavity opening with the cavity acoustic mode through an explicit force balancing relation between the two sides of the opening. The vortical motion is modeled in the potential flow framework, in which the oscillating motion of the thin shear layer is described by an array of convected point vortices, and the unsteady vortex shedding is determined by the Kutta condition. The cavity acoustic mode is obtained from the one-dimensional acoustic propagation model, the time-domain equivalent of which is given by means of a broadband time-domain impedance model. The acoustic resistances due to radiation and viscous loss at the opening are also taken into account. The physical processes of the self-excited oscillations, at both resonance and off-resonance states, are simulated directly in the time domain. Results show that the shear layer exhibits a weak flapping motion at the off-resonance state, whereas it rolls up into large-scale vortex cores when resonances occur. Single and dual-vortex patterns are observed corresponding to the first and second hydrodynamic modes. The simulation also reveals different trajectories of the two vortices across the opening when the first and second hydrodynamic modes co-exist. The strong modulation of the shed vorticity by the acoustic feedback at the resonance state is demonstrated. The model overestimates the pressure pulsation amplitude by a factor 2, which is expected to be due to the turbulence of the flow which is not taken into account. The model neglects vortex shedding at the downstream and side edges of the cavity. This will also result in an overestimation of the pulsation amplitude.