Vortex Wall Interaction Research Articles

Vortex–wall interactions in elliptic impinging synthetic jets

Vortex–wall interactions in elliptic impinging synthetic jets

MQGeometry-1.0: a multi-layer quasi-geostrophic solver on non-rectangular geometries

Abstract. This paper presents MQGeometry, a multi-layer quasi-geostrophic (QG) equation solver for non-rectangular geometries. We advect the potential vorticity (PV) with finite volumes to ensure global PV conservation using a staggered discretization of the PV and stream function (SF). Thanks to this staggering, the PV is defined inside the domain, removing the need to define the PV on the domain boundary. We compute PV fluxes with upwind-biased interpolations whose implicit dissipation replaces the usual explicit (hyper-)viscous dissipation. The discretization presented here does not require tuning of any additional parameter, e.g., additional eddy viscosity. We solve the QG elliptic equation with a fast discrete sine transform spectral solver on rectangular geometry. We extend this fast solver to non-rectangular geometries using the capacitance matrix method. Subsequently, we validate our solver on a vortex-shear instability test case in a circular domain, on a vortex–wall interaction test case, and on an idealized wind-driven double-gyre configuration in an octagonal domain at an eddy-permitting resolution. Finally, we release a concise, efficient, and auto-differentiable PyTorch implementation of our method to facilitate future developments on this new discretization, e.g., machine-learning parameterization or data-assimilation techniques.

Decay of Taylor–Green flow type initial conditions in a two-dimensional domain

Geophysical flows are often two-dimensional (2D) in nature. The decay dynamics of the canonical, symmetric initial conditions defined by the Taylor–Green (TG) flow is simulated in a 2D domain. The standard lattice Boltzmann equation method with the Bhatnagar–Gross–Krook collision model is employed. The vortex dynamics is investigated for bounded and unbounded flows with various sets of Gaussian vortices and varying Reynolds numbers. The formation of thin filaments and the generation of small-scale structures near the no-slip walls are found. To characterize the decay properties, the integral quantities, namely, kinetic energy, E(t), enstrophy, Ω(t) , and palinstrophy, P(t), are tracked as a function of the eddy-turnover-time. The initial vortex population in the domain dictates the decay rate of these integral quantities. The energy spectra, E(k), are computed to investigate the effect of domain boundaries and vortex populations on energy distribution among different length scales for Re=50000 . The evolution of TG flow in a bounded domain shows an exponent close to −3, which may be attributed to the generation of thin filaments and small-scale structures in vortex-wall interactions. Exponent changes with an increase in the vortex populations.

Characteristics of boundary-layer transition driven by diverse streamwise vortices

The present direct numerical simulations investigate the dynamics of diverse streamwise vortices in a zero-pressure gradient incompressible laminar boundary layer and the onset of turbulence. Due to the critical role of streamwise vortices in bypass transitions, we compare the transition mechanisms induced by a single vortex and vortex pairs. We initially examine the evolution of a single vortex by employing streamwise vortex profiles at two wall-normal locations. The single streamwise vortex will prompt a more rapid eruption from the bottom part of the boundary layer if moved nearer to the wall, as observed in the experimental study by Manu et al. [“Evolution of isolated streamwise vortices in the late stages of boundary-layer transition,” Exp. Fluids 48, 431–440 (2010)]. In the late stages of boundary-layer transition, the vortex–wall interaction emerges to be particularly pronounced. The second set of simulations triggers flow transition by imposing counter-rotating vortex pairs at the inlet of the computational domain. Streamwise vortex pairs with net upward flows cause intense, sporadic ejections of near-wall fluids into the boundary-layer edge, providing the first signs of inflectional instability in all considered cases. Instead of vortex–wall interactions, flow structures created by vortex pairs penetrate deeply into the inviscid region, resulting in substantial unsteady viscous-inviscid interactions. When counter-rotating vortices accompany to form a net downward flow, the initial formation of each vortex is analogous to that of a single vortex. The instability frequency and wavelength of the transitional flow produced by a vortex introduced in the middle of the boundary layer are lower than those imposed near the wall. The transitional flow generated by the vortex pair exhibits longer-wavelength instability than the single vortex cases.

On the links between unsteady separation and Nusselt number deterioration during vortex-wall interaction

A CFD study of an axisymmetric vortex ring interacting with a flat, constant-temperature, heated wall is conducted to study the physical nature of the mechanisms leading to deterioration in wall heat transfer due to the unsteady boundary layer separation resulting from vortex-wall interaction. The study utilizes a supplemental computation of a hypothetical flow configuration in which slip is allowed at the heated wall to eliminate separation of the boundary layer during the interaction. Comparison between the physical and hypothetical cases enables “isolation”, and hence understanding of the role of separation in the deterioration of Nusselt number (Nu). It is found that the nature of the near-wall upwash velocity leading to Nu deterioration is fundamentally altered by the presence of spearation. Without separation, the upwash is driven directly by the primary vortex ring. In contrast, with separation, the near-wall upwash is modified significantly by blockage from boundary layer separation and interaction with the secondary vortex ring. The modification is associated with the development of a near-wall “sublayer” that is responsible for the deterioration of Nu independent of the behavior of the overall thermal boundary layer thickness.

Instability mechanisms and intermittency distribution in adverse pressure gradient attached and separated boundary layers

Direct numerical simulation has been carried out on one attached and two separated boundary layer flows (involving small and large separation) under the influence of an adverse pressure gradient. A unified picture of the pre-transitional boundary layer for the three cases has been provided that reveals a “mixed-mode” instability, involving contribution from instability waves and streamwise streaks. A time-frequency analysis of the transitional velocity signals has been performed which shows that as the Reynolds number decreases, the character of the time traces evolves continuously from a “spotty” behavior (exhibiting distinct turbulent spots) for the attached case to a “non-spotty” behavior (involving more “uniform” distribution of turbulent fluctuations in time) for the large-separation case, encompassing the entire spectrum of transition scenarios. The variation of the intermittency factor within the transition zone is seen to compare well with the Narasimha universal intermittency distribution. We find that although the time variation of velocity for large separation is non-spotty (or more “uniform”), the spanwise variation of velocity is spotty, showing a clear clustering of high-wavenumber fluctuations separated by quasi-laminar regions. Thus, all three cases exhibit spottiness in the transition zone with different manifestations. We present a physical cartoon for the transition scenarios for the attached and separated cases, using the ideas of vortex-wall interaction and instability of spanwise vortical structures. We find that concentrated breakdown is exhibited by all the three cases near the transition onset, and the spot breakdown processes are broadly consistent with the postulates underlying the universal intermittency distribution.

Vortex–wall interaction on the β-plane and the generation of deep submesoscale cyclones by internal Kelvin Waves–current interactions

ABSTRACT In this paper, we investigate the vortex–wall interaction on the β-plane, using a submesoscale and internal waves resolving model in an idealised context. Our results bring new insights on the dynamics of oceanic mesoscale eddies as they drift toward a western boundary. We show that there exists a strong cyclone/anticyclone asymmetry in the interaction, contrary to what was suggested in previous studies: anticyclones cannot drift meridionally along the wall because of internal Kelvin Waves–current interactions. This interaction is shown to be an efficient mechanism to generate small coherent submesoscale cyclones, which can travel hundreds of kilometres into the interior of the ocean.

Large eddy simulation of self-excited oscillation inside Helmholtz oscillator

In the present study, a large eddy simulation was conducted to simulate the three-dimensional cavitation turbulence flow inside a Helmholtz oscillator under a high Reynolds number. Numerical results show reasonable agreement with available experimental observations and data. Under the validated solution strategy, the cavitation flow is visualized in a straightforward manner and indicates the primary shedding and secondary shedding induced by the shear layer and collision wall. The evolution and the interactions between cavitation and vortices are well captured and discussed in detail. The results show that flow inside the chamber can be divided into three stages, the boundaries of which are where the vortex reaches the wall surface and where a stable vortex ring is formed on the collision wall. The cavity length has an important influence on frequency, indicating that axial constraints have a greater effect on frequency than radial constraints do. A coherent structure is used to reveal the influence of vortex-wall interactions, and the structure shows that there is a close relationship between the vortex-cavitation interaction and the flow mechanism. Our work provides insight into the internal flow of the Helmholtz oscillator and represents further efforts to demonstrate the mechanism of the oscillation jet.

A computational study of vortex rings interacting with a constant-temperature heated wall

This study is motivated by understanding the connections between the vortical structures in impinging jets and the wall heat transfer. Of particular interest are: (1) examining how the stage of evolution of vortex pairing in the jet might influence the wall heat transfer, and (2) establishing correlations between the vortex characteristics and the Nusselt number (Nu) distribution. To this end, CFD simulations are conducted of three simplified model problems involving the interaction of isolated axisymmetric vortex rings with a flat, constant-temperature, heated wall. The cases represent three scenarios of vortex-wall interaction: before (Case I), during (Case II) and after (Case III) pairing. The results show that when two vortices concurrently interact with the wall and undergo pairing (Case II), a significant instantaneous enhancement in Nu is attained in comparison to that associated with a single vortex interacting with the wall (Cases I and III). However, Case II also leads to the largest subsequent decay in Nu enhancement due to the formation of a particularly strong secondary vortex. In all cases, a deterioration in Nu, relative to unsteady diffusion, is observed simultaneously with the enhancement. Notwithstanding this deterioration, the net effect of vortex-wall interaction on the heat transfer remains positive with Case II producing the highest heat transfer rate. An analysis is conducted to establish the connection between the instantaneous maximum and minimum Nu, the circulation and the radial and the wall-normal location of the core-centers of the vortices, the thermal boundary layer thickness, the boundary layer separation location and the wall shear stress.

Response of a Streamwise Vortex–Wall Interaction to Unsteady Forcing

Streamwise vortices exist in a number of engineering flows in both external and internal aerodynamics, often with undesirable effects. An experimental investigation of a streamwise vortex–wall interaction is performed through the use of a vortex-generating wing section and a suspended splitter plate. A synthetic jet actuator is implemented below the vortex, and the response of the vortex to unsteady forcing is evaluated with a focus on spatial amplification through convective instabilities. At low forcing frequencies, a large displacement of the vortex is recorded near the actuator, but with almost no spatial amplification. This behavior agrees qualitatively with transient growth studies of columnar vortices. Within a specific frequency range, it is shown that spatial amplification of the vortex displacement occurs. The range of amplified forcing frequency agrees well with predictions for the Crow instability. The vortex–wall interaction generates a secondary vortex structure that rolls up from the boundary layer. When the actuator displaces the primary vortex structure, this causes a strong dynamic reaction in the secondary structure. This occurs due to a mutual induction mechanism between the two vortices as well as a spatial oscillation of the separation point from which the secondary structure originates.

Numerical Investigation of Vortex Ring Ground Plane Interactions

The interaction between multiple laminar thin vortex rings and solid surfaces was studied numerically so as to investigate flow patterns associated with near-wall flow structures. In this study, the vortex–wall interaction was used to investigate the tendency of the flow toward recirculatory behavior and to assess the near-wall flow conditions. The numerical model shows very good agreement with previous studies of single vortex rings for the case of orthogonal impact (angle of incidence, θ = 0 deg) and oblique impact (θ = 20 deg). The study was conducted at Reynolds numbers 585 and 1170, based on the vortex ring radius and convection velocity. The case of two vortex rings was also investigated, with particular focus on the interaction of vortex structures postimpact. Compared to the impact of a single ring with the wall, the interaction between two vortex rings and a solid surface resulted in a more highly energized boundary layer at the wall and merging of vortex structures. The azimuthal variation in the vortical structures yielded flow conditions at the wall likely to promote agitation of ground based particles.

Influence of a wall on the three-dimensional dynamics of a vortex pair

In this paper, we are interested in perturbed vortices under the influence of a wall or ground plane. Such flows have relevance to aircraft wakes in ground effect, to ship hull junction flows, to fundamental studies of turbulent structures close to a ground plane and to vortex generator flows, among others. In particular, we study the vortex dynamics of a descending vortex pair, which is unstable to a long-wave instability (Crow, AIAA J., vol. 8 (12), 1970, pp. 2172–2179), as it interacts with a horizontal ground plane. Flow separation on the wall generates opposite-sign secondary vortices which in turn induce the ‘rebound’ effect, whereby the primary vortices rise up away from the wall. Even small perturbations in the vortices can cause significant topological changes in the flow, ultimately generating an array of vortex rings which rise up from the wall in a three-dimensional ‘rebound’ effect. The resulting vortex dynamics is almost unrecognizable when compared with the classical Crow instability. If the vortices are generated below a critical height over a horizontal ground plane, the long-wave instability is inhibited by the wall. We then observe two modes of vortex–wall interaction. For small initial heights, the primary vortices are close together, enabling the secondary vortices to interact with each other, forming vertically oriented vortex rings in what we call a ‘vertical rings mode’. In the ‘horizontal rings mode’, for larger initial heights, the Crow instability develops further before wall interaction; the peak locations are farther apart and the troughs closer together upon reaching the wall. The proximity of the troughs to each other and the wall increases vorticity cancellation, leading to a strong axial pressure gradient and axial flow. Ultimately, we find a series of small horizontal vortex rings which ‘rebound’ from the wall. Both modes comprise two small vortex rings in each instability wavelength, distinct from Crow instability vortex rings, only one of which is formed per wavelength. The phenomena observed here are not limited to the above perturbed vortex pairs. For example, remarkably similar phenomena are found where vortex rings impinge obliquely with a wall.

Reynolds number influence on the formation of vortical structures on a pitching flat plate

The impact of chord-based Reynolds number on the formation of leading-edge vortices (LEVs) on unsteady pitching flat plates is investigated. The influence of secondary flow structures on the shear layer feeding the LEV and the subsequent topological change at the leading edge as the result of viscous processes are demonstrated. Time-resolved velocity fields are measured using particle image velocimetry simultaneously in two fields of view to correlate local and global flow phenomena in order to identify unsteady boundary-layer separation and the subsequent flow structures. Finally, the Reynolds number is identified as a parameter that is responsible for the transition in mechanisms leading to LEV detachment from an aerofoil, as it determines the viscous response of the boundary layer in the vortex-wall interaction.

An accurate pressure–velocity decoupling technique for semi‐implicit rotational projection methods

SummaryIn this paper, an accurate semi‐implicit rotational projection method is introduced to solve the Navier–Stokes equations for incompressible flow simulations. The accuracy of the fractional step procedure is investigated for the standard finite‐difference method, and the discrete forms are presented with arbitrary orders or accuracy. In contrast to the previous semi‐implicit projection methods, herein, an alternative way is proposed to decouple pressure from the momentum equation by employing the principle form of the pressure Poisson equation. This equation is based on the divergence of the convective terms and incorporates the actual pressure in the simulations. As a result, the accuracy of the method is not affected by the common choice of the pseudo‐pressure in the previous methods. Also, the velocity correction step is redefined, and boundary conditions are introduced accordingly. Several numerical tests are conducted to assess the robustness of the method for second and fourth orders of accuracy. The results are compared with the solutions obtained from a typical high‐resolution fully explicit method and available benchmark reports. Herein, the numerical tests are consisting of simulations for the Taylor–Green vortex, lid‐driven square cavity, and vortex–wall interaction. It is shown that the present method can preserve the order of accuracy for both velocity and pressure fields in second‐order and high‐order simulations. Furthermore, a very good agreement is observed between the results of the present method and benchmark simulations. Copyright © 2016 John Wiley & Sons, Ltd.

Numerical visualization of shock tube-generated vortex–wall interaction using a fifth-order upwind scheme

Numerical visualization of shock tube-generated vortex–wall interaction using a fifth-order upwind scheme

Vortex ring behavior provides the epigenetic blueprint for the human heart.

The laws of fluid dynamics govern vortex ring formation and precede cardiac development by billions of years, suggesting that diastolic vortex ring formation is instrumental in defining the shape of the heart. Using novel and validated magnetic resonance imaging measurements, we show that the healthy left ventricle moves in tandem with the expanding vortex ring, indicating that cardiac form and function is epigenetically optimized to accommodate vortex ring formation for volume pumping. Healthy hearts demonstrate a strong coupling between vortex and cardiac volumes (R2 = 0.83), but this optimized phenotype is lost in heart failure, suggesting restoration of normal vortex ring dynamics as a new, and possibly important consideration for individualized heart failure treatment. Vortex ring volume was unrelated to early rapid filling (E-wave) velocity in patients and controls. Characteristics of vortex-wall interaction provide unique physiologic and mechanistic information about cardiac diastolic function that may be applied to guide the design and implantation of prosthetic valves, and have potential clinical utility as therapeutic targets for tailored medicine or measures of cardiac health.

High-order pole-treatment in cylindrical coordinates for incompressible flow simulations with finite-difference collocated schemes

A finite-difference collocated scheme is proposed for the simulation of unsteady incompressible flows in cylindrical coordinates. The Rhie–Chow flux-interpolation technique is used to avoid the odd–even decoupling of the pressure field. It is shown that the calculation of the Coriolis and centrifugal acceleration terms based on the cell-center values lead to numerical instabilities near the pole in the inviscid regime. To avoid this issue, a new formulation based on the combination of cell-center and cell-face velocity components is proposed for the calculation of these terms. Furthermore, a new pole treatment methodology is introduced to calculate the viscous terms, resulting single-valued properties at the pole. As regards the extensions of the present scheme to higher orders of accuracy, a fourth-order spatial discretization is also introduced and verified. Moreover, it is shown that for higher-order extensions, the present pole treatment is able to preserve the order of accuracy and the L2-norm and L∞-norm errors are greatly improved in comparison with the previous schemes. The robustness of the present method is assessed via five different numerical tests including laminar flows in a polar cavity, vortex-wall interaction, evolution of a monopole vortex-system to a tripole vortex-system, advection of the lamb dipole, and large eddy simulation (LES) of turbulent pipe flows. Compared to the previous LES results for turbulent pipe flows, significant improvement is obtained for the mean and fluctuating velocities especially at the core region of the channel. Similarly, at the wall region, the fluctuating axial and azimuthal velocities and the skewnesses of the axial and radial velocities are very close to the previous direct numerical simulation and experimental data.

Phenomena, dynamics and instabilities of vortex pairs

Our motivation for studying the dynamics of vortex pairs stems initially from an interest in the trailing wake vortices from aircraft and the dynamics of longitudinal vortices close to a vehicle surface. However, our motivation also comes from the fact that vortex–vortex interactions and vortex–wall interactions are fundamental to many turbulent flows. The intent of the paper is to present an overview of some of our recent work concerning the formation and structure of counter-rotating vortex pairs. We are interested in the long-wave and short-wave three-dimensional instabilities that evolve for an isolated vortex pair, but also we would like to know how vortex pairs interact with a wall, including both two-dimensional interactions, and also the influence of the surface on the three-dimensional instabilities. The emphasis of this presentation is on physical mechanisms by which vortices interact with each other and with surfaces, principally from an experimental approach, but also coupled with analytical studies.

Internal jet interactions in a fluidic oscillator at low flow rate

This study focuses on the internal jet interactions and the oscillation mechanism of the feedback-free fluidic oscillator at low flow rate, corresponding to a Reynolds number of 1,350 (based on exit nozzle width and average exit velocity). Particle image velocimetry (PIV) was used in this study with a refractive index-matched fluid to minimize reflections that would otherwise occur at the fluid-acrylic interface in the test setup. A simple microphone-tube sensor configuration generated a reference signal, with a phase-averaging method based on each quarter period for velocity time history reconstruction. PIV results revealed the existence of a vortex of fluctuating size, shape, and strength on each side of the oscillator; and two transient vortices that are formed in the dome region of the oscillator by each of the jets once per period. The dome vortices periodically bifurcate each of the jets and transfer some of the kinetic energy of that jet to the opposing jet. This kinetic energy transfer mechanism dictates the dominance of either jet at the exit, and this mechanism repeats itself to sustain the oscillations created by the fluidic oscillator. At this flow rate, the two jets form a continuous mutual collision, and the jets are never completely cut off from the exit. The oscillatory behavior at this flow rate is due to a complex combination of jet interactions and bifurcations, vortex–shear layer interactions, vortex–wall interactions, and saddle point formations.

Computational study of the interaction between a shock and a near-wall vortex using a weighted compact nonlinear scheme

The interaction between a moderate-strength shock wave and a near-wall vortex is studied numerically by solving the two-dimensional, unsteady compressible Navier–Stokes equations using a weighted compact nonlinear scheme with a simple low-dissipation advection upstream splitting method for flux splitting. Our main purpose is to clarify the development of the flow field and the generation of sound waves resulting from the interaction. The effects of the vortex–wall distance on the sound generation associated with variations in the flow structures are also examined. The computational results show that three sound sources are involved in this problem: (i) a quadrupolar sound source due to the shock–vortex interaction; (ii) a dipolar sound source due to the vortex–wall interaction; and (iii) a dipolar sound source due to unsteady wall shear stress. The sound field is the combination of the sound waves produced by all three sound sources. In addition to the interaction of the incident shock with the vortex, a secondary shock–vortex interaction is caused by the reflection of the reflected shock (MR2) from the wall. The flow field is dominated by the primary and secondary shock–vortex interactions. The generation mechanism of the third sound, which is newly discovered, due to the MR2–vortex interaction is presented. The pressure variations generated by (ii) become significant with decreasing vortex–wall distance. The sound waves caused by (iii) are extremely weak compared with those caused by (i) and (ii) and are negligible in the computed sound field.