Three-dimensional Shear Layer Research Articles

Aeroacoustics and shear layer characteristics of confined cavities subject to low Mach number flow

Numerous engineering applications involve low Mach number flow in cavity aperture geometries, which can generate flow-excited acoustic oscillations and hence high amplitudes of noise and vibration. This is caused by the instability of the shear layer interacting with the acoustic modes of the system. In this study, we experimentally investigate ducted cylindrical cavities with aspect ratios (Depth/Diameter) of 0.5, 1, and 1.5 up to flow velocities of Mach 0.4. We examine the influence of the cavity confinement (Cavity Width/Duct Width) on the aeroacoustics response, as well as the downstream impingement behaviour of the shear layer. Rectangular and square cavities bearing similar geometric parameters are also investigated to compare the effect of the cavity shape on the shear layer dynamics and the aeroacoustics response. The results confirm resonance behaviour at frequencies well predicted by the theory, as well as Strouhal periodicities that agree with reported literature. However, cylindrical and square cavities with aspect ratio of 0.5 exhibit stronger dependence on the aspect ratio due to the interference of the recirculation region by the cavity floor, ultimately modifying the symmetry of the shear layer. This asymmetric flow pattern affects the velocity-dependent tones, generating much lower Strouhal numbers than the estimated values, and must be accounted for in equipment design. Moreover, Particle Image Velocimetry (PIV) measurements further illustrate the spatial characteristics of the shear layer dynamics for the various shaped cavities. The visualizations demonstrate enhanced flow modulation at higher acoustic pressure amplitudes, as well as reveal the flow asymmetry and the three-dimensional shear layer topology in cylindrical and square cavities.

Performance enhancement of the wavy cylinder-based piezoelectric wind energy harvester with different wave-shaped attachments

The vortex-induced vibration (VIV)-based piezoelectric wind energy harvester (PWEH) has a small working bandwidth and poor wind energy harvesting performance. In order to improve the output power of the PWEH and achieve sustainable power supply for microelectronic products, this study proposes a novel wavy cylinder-based PWEH with two wavy attachment rods attached to the surface of the wavy cylinder, the mathematical model of PWEH is developed. The flow-induced vibration (FIV) response mechanism and the energy harvesting characteristics of the wavy cylinder-based PWEH are numerically explored. The wavy cylinder with wavy-shaped attachments produces a three-dimensional shear layer that can increase the wavy cylinder’s aeroelastic instability range and realize the synergistic effects of VIV and galloping, which increases the wave cylinder’s vibrational amplitude and lowers the galloping critical wind speed. Compared with the typical VIV-PWEH, the novel wind energy harvester can work outside the VIV lock-in range, and its output power and voltage rise as wind speed does. The wavy attachment rods with triangular cross section have greater advantages than other rods, its output power is 6.13 mW at a wind speed of 5.7 m/s and load resistance of 100 KΩ, compared with the circular cylinder PWEH, the average power increases by approximately 166%. The study’s findings can theoretically promote the enhancement of PWEH’s energy harvesting efficiency.

Publisher's Note: “Reacting and non-reacting, three-dimensional shear layers with spanwise stretching” [Phys. Fluids 34, 123602 (2022)

Publisher's Note: “Reacting and non-reacting, three-dimensional shear layers with spanwise stretching” [Phys. Fluids <b>34</b>, 123602 (2022)

Reacting and non-reacting, three-dimensional shear layers with spanwise stretching

A three-dimensional, steady, laminar shear-layer flow spatially developing under a boundary-layer approximation with mixing, chemical reaction, and imposed normal strain is analyzed. The purpose of this study is to determine conditions by which certain stretched vortex layers appearing in turbulent combustion are the asymptotic result of a spatially developing shear flow with imposed compressive strain. The imposed strain creates a counterflow that stretches the vorticity in the spanwise direction. Equations are reduced to a two-dimensional form for three velocity components. The non-reactive and reactive cases of the two-dimensional form of the governing equations are solved numerically, with consideration of several parameter inputs, such as the Damköhler number, the Prandtl number, chemical composition, and free-stream velocity ratios. The analysis of the non-reactive case focuses on the mixing between hotter gaseous oxygen and cooler gaseous propane. The free-stream strain rate κ* is predicted by ordinary differential equations based on the imposed spanwise pressure variation. One-step chemical kinetics are used to describe diffusion flames and multi-flame structures. The imposed normal strain rate has a significant effect on the width of downstream mixing layers as well as the burning rate. Asymptotically in the downstream direction, a constant width of the shear layer is obtained if the imposed normal strain rate is constant. The one-dimensional asymptotic result is an exact solution to the multicomponent Navier–Stokes equation for both reacting and non-reacting flows, although it was obtained using the boundary-layer approximation. A similar solution with the layer width growing with the square root of downstream distance is found when the imposed strain rate decreases as the reciprocal of downstream distance. The reduced-order asymptotic solutions can provide useful guidance in developing flamelet models for simulations of turbulent combustion.

Numerical simulations and analysis of the turbulent flow field in a practical gas turbine engine combustor

The turbulent flow field in a practical gas turbine combustor is very complex because of the interactions between various flows resulting from components like multiple types of swirlers, dilution holes, and liner effusion cooling holes. Numerical simulations of flows in such complex combustor configurations are challenging. The challenges result from (a) the complexities of the interfaces between multiple three-dimensional shear layers, (b) the need for proper treatment of a large number of tiny effusion holes with multiple angles, and (c) the requirements for fast turnaround times in support of engineering design optimization. Both the Reynolds averaged Navier–Stokes simulation (RANS) and the large eddy simulation (LES) for the practical combustor geometry are considered. An autonomous meshing using the cut-cell Cartesian method and adaptive mesh refinement (AMR) is demonstrated for the first time to simulate the flow in a practical combustor geometry. The numerical studies include a set of computations of flows under a prescribed pressure drop across the passage of interest and another set of computations with all passages open with a specified total flow rate at the plenum inlet and the pressure at the exit. For both sets, the results of the RANS and the LES flow computations agree with each other and with the corresponding measurements. The results from the high-resolution LES simulations are utilized to gain fundamental insights into the complex turbulent flow field by examining the profiles of the velocity, the vorticity, and the turbulent kinetic energy. The dynamics of the turbulent structures are well captured in the results of the LES simulations.

Numerical study of the suction flow control of the supersonic boundary layer transition in a framework of gas-kinetic scheme

In this paper, we numerically study the supersonic boundary layer transition process and the suction flow control method by employing the DNS technology. By adopting the high resolution GKS method, the mechanism of the boundary transition and the statistical characteristics of the compressible turbulent boundary layer are investigated. Results indicate that the streamwise vortex and the three-dimensional shear layer with high instability are the main causes of the boundary layer transition. Suction control cases show that the laminar boundary layer suction can weaken the development of the unstable disturbance waves in the boundary layer, and delay the streamwise position of the local disturbance. Also, the space distributions of the vortex structure are weakened to delay the process of the transition.

Evolution of a quasi-two-dimensional shear layer in a soap film flow

A quasi-two-dimensional shear layer is produced by merging two gravity-driven flows of soap film at different average velocities. The Kelvin–Helmholtz instability dominates the evolution of the shear layer, similar to what is observed in three-dimensional shear layers. However, the constraints that effectively limit the flow to two spatial dimensions have a considerable influence on the development of secondary instabilities and transition to turbulence. Nearly 40 cm downstream in the flow, two two-dimensional instabilities are observed, namely, vortex-pairing and secondary Kelvin–Helmholtz instability. The development of secondary instabilities and transition to turbulence in the flow is also affected by the interaction of the flowing soap film with boundary layers forming in the air surrounding the flowing soap film in the direction normal to the plane of the film. This becomes apparent when the flow is analyzed quantitatively in terms of the mixing interface length and fractal dimension. Initially, the mixing interface length grows exponentially with the downstream distance; however, beyond a certain distance, the growth stops. For the fractal dimension of the mixing interface in our quasi-two-dimensional shear layer, we have observed a peak value of 1.27 as compared to 1.34 reported in the literature for a corresponding section of a three-dimensional shear layer. For scales larger than ∼1 cm, interaction with air begins to dominate as the leading mechanism of dissipation. Coupling with boundary layers in air near the soap film drains energy from the large flow features and apparently “freezes” its evolution, producing “fossil” turbulence at large downstream distances.

Experimental study on suppressing vortex-induced vibration of a long-span bridge by installing the wavy railings

It is known that vortex shedding behind bluff bodies can be suppressed by introducing some three-dimensional geometric disturbance. Therefore, a new passive control device named wavy railings is proposed to mitigate the vortex-induced-vibration (VIV) of a single box section bridge. The wavy railing is composed of vertical posts and wavy crossbars, which can provide three-dimensional perturbation to the flow field and then lead to the development of a three-dimensional free shear layer which does not roll up into a vortex street and hence suppress the VIV. In this study, the control effects of the wavy railings on mitigating VIV are investigated through wind tunnel tests. The results reveal that when the wavelength of the wavy bar is 0.5H or 1H (H is the height of the bridge deck), both vertical and torsional VIV can be completely suppressed, and the upper surface edge is the optimal installation position.

Effects of free-stream turbulence intensity on transition in a laminar separation bubble formed over an airfoil

The laminar-to-turbulent transition process in a laminar separation bubble formed over a NACA 0018 airfoil is investigated experimentally. All experiments are performed for an angle of attack of 4 $$^{\circ }$$ , chord Reynolds numbers of 80,000 and 125,000, and free-stream turbulence intensities between 0.06 and 1.99%. The results show that increasing the level of free-stream turbulence intensity leads to a decrease in separation bubble length, attributed to a downstream shift in mean separation and an upstream shift in mean reattachment, the later ascribed to an upstream shift in mean transition. Maximum spatial amplification rates of disturbances in the separated shear layer decrease with increasing free-stream turbulence intensity, implying that the larger initial amplitudes of disturbances are solely responsible for the upstream shift in mean transition and as a result mean reattachment. At the baseline level of turbulence intensity, coherent structures forming in the aft portion of the bubble are characterized by strong spanwise coherence at formation, and undergo spanwise deformations leading to localized breakup in the vicinity of mean reattachment. As the level of free-stream turbulence intensity is increased, the spanwise coherence of the shear layer rollers is reduced, and spanwise undulations in the vortex filaments start to take place at the mean location of roll-up. At the highest level of turbulence intensity investigated, streamwise streaks originating in the boundary layer upstream of the separation bubble are observed within the bubble. These streaks signify an onset of bypass transition upstream of the separation bubble, which gives rise to a highly three-dimensional shear layer roll-up. A quantitative analysis of the associated changes in salient characteristics of the coherent structures is presented, connecting the effect of elevated free-stream turbulence intensity on the time-averaged and dynamic characteristics of the separation bubble.

Control of a three-dimensional turbulent shear layer by means of oblique vortices

The effect of local forcing on the separated, three-dimensional shear layer downstream of a backward-facing step is investigated by means of large-eddy simulation for a Reynolds number based on the step height of 10,700. The step edge is either oriented normal to the approaching turbulent boundary layer or swept at an angle of $$40^\circ $$ . Oblique vortices with different orientation and spacing are generated by wavelike suction and blowing of fluid through an edge parallel slot. The vortices exhibit a complex three-dimensional structure, but they can be characterized by a wavevector in a horizontal section plane. In order to determine the step-normal component of the wavevector, a method is developed based on phase averages. The dependence of the wavevector on the forcing parameters can be described in terms of a dispersion relation, the structure of which indicates that the disturbances are mainly convected through the fluid. The introduced vortices reduce the size of the recirculation region by up to 38%. In both the planar and the swept case, the most efficient of the studied forcings consists of vortices which propagate in a direction that deviates by more than $$50^\circ $$ from the step normal. These vortices exhibit a spacing in the order of 2.5 step heights. The upstream shift of the reattachment line can be explained by increased mixing and momentum transport inside the shear layer which is reflected in high levels of the Reynolds shear stress $$-\rho \overline{u'v'}$$ . The position of the maximum of the coherent shear stress is found to depend linearly on the wavelength, similar to two-dimensional free shear layers.

Hypersonic transition induced by three isolated roughness elements on a flat plate

Hypersonic boundary layer transition from laminar to turbulent induced by three isolated roughness elements (ramp, diamond, and cylinder) was investigated by direct numerical simulations based on finite volume formulation with high order MDCD scheme. The effects of roughness shape on the transition mechanism, aerodynamic and aero-thermodynamic performances were quantitatively compared. The transition is dominated by three-dimensional shear layer instability and the streamwise transition locations are almost the same for all three roughness elements. The width of turbulent wake, the drag increment and the heat flux are the largest for cylinder. At the same time, the turbulent wake is the narrowest and drag and heat flux are the lowest for the ramp.

Secondary instability analysis of crossflow on a hypersonic yawed straight circular cone

The purpose of this paper is to provide secondary instability analysis of stationary crossflow vortices on a hypersonic yawed straight circular cone with a $7^{\circ }$ half-angle at $6^{\circ }$ angle of attack, free-stream Mach number 6 and unit Reynolds number $10.09\times 10^{6}~\text{m}^{-1}$. At an angle of attack, a three-dimensional boundary layer is developed between the windward and leeward symmetry planes. Under the action of azimuthal pressure gradients, the flow near the surface is deflected more than the flow near the edge of the boundary layer. This results in an inflectional velocity profile that can sustain the growth of crossflow vortices. The stationary crossflow instability is computed by means of the nonlinear parabolized stability equations, including a methodology to predict the stationary-crossflow marching path and variation of the spanwise number of waves in the marching direction solely from the basic state. Secondary instability analysis is performed using spatial BiGlobal equations based on two-dimensional partial differential equations. The secondary instabilities are calculated at different axial locations along two crossflow vortex trajectories selected to complement experiments conducted in the Mach 6 Quiet Tunnel at Texas A&amp;M University and in the Boeing/AFOSR Mach 6 Quiet Tunnel at Purdue University. The secondary instability analysis captures various instability modes. Similar to observations in the low-speed regime for an infinite swept wing, secondary shear-layer instabilities are amplified as a consequence of the three-dimensional shear layer formed by crossflow vortices. Also, low-frequency travelling crossflow and high-frequency second modes coexist with the shear-layer instabilities. These results are shown to be in good agreement with the two sets of hypersonic yawed cone experiments (one with natural surface roughness and one with artificial discrete roughness) and compare well with experimental measurements of an incompressible swept wing.

Influence of artificial viscosity on the formation of vortex cascades in the shear layer

Numerical analysis of development of vortex cascades in a three-dimensional inviscid shear layer depending on the method of determining and the value of artificial viscosity is done. At the developed stage of turbulence the spectral analysis of kinetic energy is carried out and the law -5/3 of Kholmogorov is confirmed. Pulsation and correlation functions of the flow are investigated.

Global Stability Analyses Unraveling Roughness-induced Transition Mechanisms

The linear global instability and resulting transition to turbulence induced by a cylindrical roughness element of height h and diameter d = 3h immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and three-dimensional stability analyses. The configuration investigated is the same as the one in- vestigated experimentally by Fransson et al.10. Base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each side. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. For the set of parameters considered, it is able to sustain a varicose global instability for which the predicted critical Reynolds number is only 6% larger than the one reported in Ref. 10. A kinetic energy budget and wavemaker analysis revealed that this mode finds its root in the reversed flow region right downstream the roughness element and extracts most of its energy from the central low-speed region and streaks further downstream. Direct numerical simulations of the flow past this roughness element puts in the limelight the ability for this linear instability to give birth to hairpin vortices and thus trigger transition to turbulence.

Characteristics of Flow around a Modified Square Prism

The present investigations focus attention on PIV measurements and three-dimensional numerical investigation on flow past a modified square prism with a sinusoidal surface. The detailed near wake vortex structures and velocity fields of such modified square prism are captured and compared with a straight square prism in the same flow conditions. The three-dimensional free shear layers behind the modified square prism extend further downstream and become more stable than those of the straight one. For a modified square prism, significant mean drag coefficient reduction and fluctuating lift suppression are obtained at the Reynolds numbers of 600 and 5900. It indicates that such modified square prism is capable of minimization of flow induced vibration and force reduction.

Stabilisation of the Absolute Instability of a Flow Past a Cylinder via Spanwise Forcing at Re = 180

Vortex shedding in the wake of bluff bodies is often an undesired phenomenon which generates unsteady loads, vibrations and fluctuations of the aerodynamic forces. Consequently, the attenuation or suppression of the self-sustained oscillations associated to the vortex shedding is a fundamental problem in a wide range of engineering applications. Three-dimensional control techniques to control the vortex shedding are characterised by a variation of the control input along the spanwise direction and offer a promising methodology due to their versatility and high potential efficiency 1. In the present paper, the control of vortex dynamics of the wake of a flow past a cylinder at Reynolds number Re = 180 is performed by means of spanwise distributed forcing 1 2; starting from a fully developed shedding, a sufficiently high spanwise forcing is introduced on the surface of the cylinder, close to the separation regions, to stabilise the near-wake in a time-independent state, similarly to the effect of a sinusoidal stagnation surface 3,4. The effects of the forcing on the drag reduction and the dynamics of the vorticity have been investigated using a spanwise gaussian forcing, which generates a significant redistribution of the spanwise vorticity into streamwise and vertical components was ob- served, leading to a minor susceptibility of the three-dimensional shear layers to roll-up into the vortex street 4? . An insight into the main physical mechanisms underlying the suppression is provided by the hydrodynamic stability theory. Three different regimes were found for different forcing amplitude and the computation of the leading modes helps to shed light on some mechanisms responsible for the suppression of the Von-Karman shedding.

Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations

AbstractThe linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height $h$ and diameter $d$ immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each of its sides. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar–turbulent transition process. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes is related to a different physical mechanism. While the varicose mode has its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and has its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability: whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake region, for larger roughness elements the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio ${\it\eta}=1$ (with ${\it\eta}=d/h$) roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff–Braslow transition diagram provides qualitatively good agreement.

The Vortical Structures in the Rear Separation and Wake Produced by a Supersonic Micro-Ramp

The vortical structures in the rear separation and wake region produced by a micro-ramp that immersed in a supersonic turbulent boundary layer are investigated. The small scale separation close to the trailing edge was revealed and this confirms the previous experimental observation. Between the reverse region and surrounding fast moving flow, a three-dimensional shear layer was formed, and vortices are generated. By using vortex line method, the spiral points were illustrated as the cross-sections of the Ω-shaped vortices that follow the shape of the separation. The vortical structure was analogous to that in the wake region, where similar Ω-shaped vortex which follows the deficit region caused by the micro-ramp can be observed. Finally, the revealed flow topology was conceived new and beneficial to the studying of wall bounded turbulence which involves similar vortical structures but in a smaller scale, compared with the vortical pattern in the current micro-ramp wake.

Laminar–turbulent transition induced by a discrete roughness element in a supersonic boundary layer

AbstractThe linear instability and breakdown to turbulence induced by an isolated roughness element in a boundary layer at Mach $2. 5$, over an isothermal flat plate with laminar adiabatic wall temperature, have been analysed by means of direct numerical simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is crucial to prediction of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary layer displacement thickness, generates a highly unstable wake, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer and is able to sustain the rapid growth of a number of instability modes. The most unstable of these modes are associated with varicose or sinuous deformations of the low-velocity streak; they are a consequence of the instability developing in the three-dimensional shear layer as a whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most unstable wake mode is of the varicose type and grows on average ${\sim }17\hspace{0.167em} \% $ faster than the most unstable sinuous mode and ${\sim }30$ times faster than the most unstable boundary layer mode occurring in the absence of a roughness element. Due to the high growth-rates registered in the presence of the roughness element, an amplification factor of $N= 9$ is reached within ${\sim }50$ roughness heights from the roughness trailing edge. The independently performed Navier–Stokes, spatial BiGlobal and PSE-3D stability results are in excellent agreement with each other, validating the use of simplified theories for roughness-induced transition involving wake instabilities. Following the linear stages of the laminar–turbulent transition process, the roll-up of the three-dimensional shear layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate similar to that observed in the case of compressible turbulent spots for the same Mach number.

Numerical study of flow patterns and force characteristics for square and rectangular cylinders with wavy surfaces

This paper presents a numerical study of three-dimensional flow around wavy rectangular cylinders with sinusoidal variations in cross-section area along the spanwise direction over wide Reynolds number regimes. The detailed near wake vortex structures and force characteristics of the wavy rectangular cylinder are captured and the influence of length-to-thickness ratio ( L/ D m =1 to 8) of the wavy rectangular cylinder is discussed and compared with a plain straight rectangular cylinder with the same size and flow conditions. Experimental measurements were also performed for the validation of the present numerical results using the PIV technique. For a square cylinder ( L/ D m =1), significant force reduction occurs for a wavy square cylinder compared with a straight square cylinder. The three-dimensional free shear layers behind the wavy square cylinder are more stable than those of the straight square cylinder. For a rectangular cylinder ( L/ D m ≥2), several vortex shedding patterns can be observed. The free shear layers exhibit a steady flow feature with symmetrical flow patterns behind the wavy cylinder for Re=100. At Re=500, the mean drag coefficient and the fluctuating lift coefficient of the wavy rectangular cylinders are greatly suppressed compared to a plain straight cylinder, while such advantageous features gradually disappear with the increase of the aspect ratio and Reynolds number. At Re=5000, the advantageous characteristics on flow control disappear for wavy cylinders with L/ D m >2 due to breaking down of the periodic repeated additional transverse vortices. Finally, a wavy cylinder L/ D m =8, with an angle of incidence α=15° is studied. Results show that such wavy surface does not possess a significant advantage in flow separation control.