Shear Layer Research Articles

Effects of aspect ratio on flow characteristics on free surface-mounted rectangular cylinders

Turbulent flow characteristics around free surface-mounted rectangular cylinders of different streamwise aspect ratios (AR=1, 2, 2.5, 3, 4, 5, and 8 denoted as AR1, AR2, AR2.5, AR3, AR4, AR5, and AR8, respectively) at a Reynolds number based on the freestream velocity and cylinder height, Reh = 11100, were investigated experimentally using a time-resolved particle image velocimetry system. The results reveal distinct flow behaviors for different aspect ratios. The separated shear layer is shed directly into the wake for AR1, while AR2 and AR2.5 exhibits intermittent reattachment on the cylinder and direct shedding into the wake. However, for AR≥3 cylinders, the separated shear layer reattaches onto the cylinder and is later shed into the wake after subsequent separation from the trailing edge of the cylinder. Comparative analysis with previous studies on rectangular cylinders in uniform flow and wall-mounted conditions demonstrates similarities in reattachment behavior on the cylinder to uniform flow cases and wake reattachment mechanism akin to wall-mounted cylinders subjected to a thin turbulent boundary layer. The Reynolds stresses, turbulence production, and vortex shedding patterns examined with frequency spectra and proper orthogonal decomposition of velocity fluctuations exhibit significant dependence on streamwise aspect ratio.

Responses to disturbance of supersonic shear layer: Input-output analysis

Responses to disturbance of supersonic shear layer: Input-output analysis

Experimental and Numerical Study on the Plasma-Laser-Induced Ignition of Strut Stabilizer at Different Locations

The minimum ignition equivalence ratio of the strut stabilizer is an important parameter in the design of integrated afterburners. The ignition location significantly affects the ignition equivalence ratio and flame propagation, and therefore, it should be deeply studied. The ignition equivalence ratio and flame propagation at different axial ignition locations downstream of the strut stabilizer are studied in this paper. When the ignition distance is approximately the bluff body trailing edge width, a lower ignition equivalence ratio is required for ignition, and the flame propagates faster through the entire combustion chamber. For different ignition locations, the generated flame kernel at different locations all first propagates to the shear layer. Subsequently, the unilateral flame rapidly extends, ultimately igniting the entire combustion chamber. The flame propagation trajectory depends on the ignition location controlled by the non-reacting flow field and the distribution of kerosene concentration. The flame propagation trajectory mainly includes three paths: (1) the flame kernel is directly downstream the shear layer when the ignition location is close to the tail edge of the stabilizer, (2) the flame propagates upstream into the shear layer in a U-shape when the ignition location is far from the stabilizer but still in the recirculation zone, and (3) the flame propagates upstream into the recirculation zone and shear layer in a U-shape when the ignition location is outside the recirculation zone. In addition, the time for flame propagation to the shear layer is directly related to the ignition performance when the ignition location is within the recirculation zone. If the flame reaches the shear layer in a longer time, there will be more energy loss during the flame propagation process, and the ignition performance will deteriorate. The speed of the flame-trailing edge extension is directly related to the ignition fuel-air ratio, and the downstream extension of the flame is mainly affected by the turbulence velocity in the shear layer.

Direct numerical simulation of 45° oblique flow past surface-mounted square cylinder

Comprehensive coherent structures around a surface-mounted low aspect ratio square cylinder in uniform flow with an oblique angle of $45^{\circ }$ were investigated for cylinder-width-based Reynolds numbers of 3000 and 10 000 by direct numerical simulation based on a topology-confined mesh refinement framework. High-resolution simulations and the critical-point concept were scrutinized to reveal for the first time the reasonable and compatible topologies of flow separation and complete near-wall structures, due to their extensive impact on various engineering applications. Large-scale horseshoe vortices are observed at two notable foci in the viscous sublayer. Within this layer, a wall-parallel jet is formed by downflow intruding into the bottom surface at the half-saddle point, then deflecting in the upstream direction and finally penetrating the bottom surface until the half-saddle point. A pair of conical vortices on the cylinder's top surface switch themselves on two sides of the square cylinder, where the switching frequency is identical with that of the sway of the side shear layer. The undulation of the Kelvin–Helmholtz instability is identified in the instantaneous development of a conical vortex and side shear layer, where the scaling of the ratio of the Kelvin–Helmholtz and von Kármán frequencies follows the power-law relation obtained by Lander et al. (J. Fluid Mech., vol. 849, 2018, pp. 1096–1119). Large-scale arch-shaped vortex is often detected in the intermediate wake region of a square cylinder, involving two interconnected portions, such as the leg portion separated from leeward surfaces and head portion rolled up from the top surface. The leg portion of the arch-shaped vortex was rooted by two foci near the bottom-surface plane.

Dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor.

We numerically study the dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor using analytical methodologies based on dynamical systems theory, symbolic dynamics, complex networks, and machine learning. The global dynamic behavior of a heat release rate field represents low-dimensional chaotic oscillations with deterministically aperiodic intercycle dynamics. Spray combustion instability is driven in the formation and separation region of a large-scale organized vortex induced by the hydrodynamic shear layer instability at the edge of the backstep. This region corresponds fairly to that of the hub in an acoustic-energy-flux-based spatial network. The feature importance in a random forest is valid for clarifying the feedback coupling of spray combustion instability.

Experimental evaluation of the flow field induced by an active vortex generator

This investigation examined the flow field generated by a ramp-shaped vortex generator (VG) that underwent active oscillation within a laminar boundary layer. The oscillations were applied through a servomotor, which pivoted the VG around its leading edge. The study evaluated the influence of varying the maximum VG height during the oscillations (h), actuation frequency (f), and the waveform governing the periodic oscillation of the VG. Planar particle image velocimetry (PIV) measurements were conducted to estimate flow mixing and the drag induced by the VG. The height-based Reynolds number (Reh) ranged from 300 to 600, and the chord-based Strouhal number (Stc) for the oscillations varied from 0.67 to 3.33. The findings of the study indicate that active VGs lead to a greater wall-normal transport of streamwise momentum and result in lower drag compared to static VGs. Furthermore, increasing h results in larger momentum transport and drag of the active VGs. The investigation also revealed that the highest momentum transport and drag occurred when f was close to the instability frequency of the shear layer. The results show the potential of active VGs for separation control under various flow conditions.

Comparison of fluid structure downstream of an evaporative flameholder with subsonic uniform and subsonic-supersonic inflows

Subsonic uniform and supersonic mixing flows are widely present in the combustion chamber of a multi-mode combined scramjet engine, where the significant pressure, velocity, and temperature gradients of the two impose severe limitations on flame propagation. The vortex structures downstream of an evaporative flameholder were experimentally measured under subsonic-supersonic mixing inflow and subsonic uniform inflow. Results indicate that, under subsonic-supersonic mixing inflow conditions, an asymmetric vortex structure in the recirculation zone is formed due to the presence of a subsonic-supersonic shear layer, which exerts compressive or stretching effects on the recirculation zone downstream of the flameholder, in contrast to the symmetric dual-vortex structure observed under subsonic uniform inflow conditions. The asymmetric recirculation zone displays fluid being entrained from one vortex to another, with the degree and direction of entrainment dependent on the supersonic expansion state. Additionally, a simplified flow field structure is proposed for comparing the differences between the subsonic-supersonic mixing inflow and subsonic uniform inflow, along with the introduction of five regions and two stages to describe the flow field structure downstream of the flameholder under subsonic-supersonic mixing inflow. Analysis of the flow characteristics downstream of the flameholder under subsonic-supersonic mixing inflow and subsonic uniform inflow conditions can offer design insights for the combustion scheme of aerospace-integrated propulsion systems.

Identifying optimal location for control of thermoacoustic instability through statistical analysis of saddle point trajectories.

We propose a framework of Lagrangian Coherent Structures (LCSs) to enable passive open-loop control of tonal sound generated during thermoacoustic instability. Experiments were performed in a laboratory-scale bluff-body stabilized turbulent combustor in the state of thermoacoustic instability. We use dynamic mode decomposition on the flow-field to identify dynamical regions where the acoustic frequency is dominant. We find that the separating shear layer from the backward-facing step of the combustor envelops a cylindrical vortex in the outer recirculation zone, which eventually impinges on the top wall of the combustor during thermoacoustic instability. We track the saddle points in this shear layer emerging from the backward-facing step over several acoustic cycles. A passive control strategy is then developed by injecting a steady stream of secondary air targeting the identified optimal location where the saddle points spend a majority of their time in a statistical sense. After implementing the control action, the resultant flow-field is also analyzed using LCS to understand the key differences in flow dynamics. We find that the shear layer emerging from the dump plane is deflected in a direction almost parallel to the axis of the combustor after the control action. This deflection, in turn, prevents the shear layer from enveloping the vortex and impinging on the combustor walls, resulting in a drastic reduction in the amplitude of the sound produced.

Simulations of design and high load operation of a model Francis turbine using bridged approach to turbulence modelling

Abstract Off-design operation of hydraulic turbines is contemporarily frequented for balance of variable energy intermittence in the electric grid. Being operationally highly flexible, these turbines allow a quick transition to off-design operation from the design point. However, such operational flexibility, and therefore the grid balancing capability is impeded by generation of flow instabilities like vortex breakdown during off-design operation. Vortex breakdown causes losses in efficiency and pressure recovery, pressure fluctuations and possibly mechanical vibrations in event of resonance between system natural and flow field fluctuation frequencies. While substantial experimental and numerical effort has already been made to study draft tube vortex breakdown, an accurate numerical flow characterization of the phenomenon is still a challenge. To this end, operation of a high head model Francis turbine under design and high load regimes using a bridged turbulence modelling approach is simulated. The approach allows a seamless transition between direct numerical simulation and Reynolds averaged Navier-Stokes equations. The highest attainable accuracy is limited by the mesh size. As such a satisfactory compromise between desired accuracy and invested computational effort is attained. The flow in the draft tube is free of anomalies under design specified operation. However, at high load an axial flow stagnation occurs centrally, and the flow is separated about the stagnated zone. The core of the vortex is enlarged with flow recirculation within it. Shear layers between the central stagnant zone and surrounding outflow kink and roll up transforming it into a spiral structure. In this work, a basic yet accurate numerical flow characterization of the aforementioned flow situations is achieved.

Body length determines flow refuging for rainbow trout (Oncorhynchus mykiss) behind wing dams.

Complex hydrodynamics abound in natural streams, yet the selective pressures these impose upon different size classes of fish are not well understood. Attached vortices are produced by relatively large objects that block freestream flow, which fish routinely utilize for flow refuging. To test how flow refuging and the potential harvesting of energy (as seen in Kármán gaiting) vary across size classes in rainbow trout (Oncorhynchus mykiss; fingerling, 8 cm; parr, 14 cm; adult, 22 cm; n=4 per size class), we used a water flume (4100 l; freestream flow at 65 cm s-1) and created vortices using 45deg wing dams of varying size (small, 15 cm; medium, 31 cm; large, 48 cm). We monitored microhabitat selection and swimming kinematics of individual trout and measured the flow field in the wake of wing dams using time-resolved particle image velocimetry (PIV). Trout of each size class preferentially swam in vortices rather than the freestream, but the capacity to flow refuge varied according to the ratio of vortex width to fish length (WV:LF). Consistent refuging behavior was exhibited when WV:LF≥1.5. All size classes exhibited increased wavelength and Strouhal number and decreased tailbeat frequency within vortices compared with freestream, suggesting that swimming in vortices requires less power output. In 17% of the trials, fish preferentially swam in a manner that suggests energy harvesting from the shear layer. Our results can inform efforts toward riparian restoration and fishway design to improve salmonid conservation.

Effects of doors on an open cavity flow at Mach number 6

Open cavities with different door-opening angles are investigated using high-speed schlieren visualization and dynamic pressure measurements in hypersonic flow with a freestream Mach number of 6. With the help of numerical simulations, the shear layer deformation and pressure increase in the cavities due to the impingement of the door-leading-edge shocks are identified via comparison with those in the cavity without doors. As the door-opening angle decreases from 90°, the shear layer above the forepart of the cavity is gradually raised by the high pressure in the cavity. When the door-opening angle decreases to 30°and 15°, the boundary layer on the upstream flat plate of the cavity separates, and separation shock is observed. The doors enhance the instability of the cavity flow and increase the pressure fluctuations in the cavities. A new oscillation pattern, referred to as coupled oscillation, is observed in the cases with separation on the upstream flat plate, in which the separation shock oscillates at the same dominant frequency as the flow inside the cavity. Compared with the cavity without doors, this coupled oscillation causes a lower oscillation frequency and a larger overall sound pressure level. Cross-correlation analyses between pressure signals indicate that the disturbances generated at the trailing edge of the cavity can propagate to the separation on the upstream flat plate and cause coupled oscillation of the separation shock. The fundamental frequencies of the coupled oscillations can be normalized to approximately the same Strouhal number as that of the cavity without doors. These findings support that the oscillation mechanisms of hypersonic cavities without and with doors are primarily dominated by acoustic feedback.

Compressibility effect on flow characteristics over a circular cylinder at Reynolds number of 3900

The compressibility effect of flow over a circular cylinder has been investigated using wall-resolved large eddy simulation. The Reynolds number in terms of the freestream quantities and the cylinder diameter is fixed at 3900 while varying the freestream Mach number from 0.01 to 0.5. Mesh quality, numerical scheme, and subgrid-scale model are carefully verified prior to the detailed flow study. Results such as Mach number effects on the drag coefficient, the shape of the mean streamwise velocity profile in the near-wake, the length of the recirculation zone, and shear layer instability are provided. Although compressibility suppresses the Kelvin–Helmholtz instability and mixing process within the shear layer, it increases the velocity fluctuation in the boundary layer and the pressure difference between the freestream and recirculation zone, which intensifies the wake oscillation, shedding amplitude, thus shortens the recirculation zone significantly with the Mach number up to 0.5. This phenomenon is different from that found in lower Reynolds number cases where the length of the recirculation zone elongates as the Mach number increases. The deficit of the velocity profile shape in the near-wake depends on the length of the recirculation zone. Furthermore, inside the wake zone and near the cylinder back wall, two pairs of recirculation bubbles emerge as the Mach number increases.

Three-Dimensional Nature of Low-Frequency Unsteadiness in a Turbulent Separation Bubble

Three-dimensional behavior of low-frequency unsteadiness in the incompressible turbulent separation bubble (TSB) produced by a wall-mounted hump is investigated using time-resolved planar and stereoscopic particle image velocimetry measurements at several planes across the separated region. The aspect ratio (wind tunnel width/separation length, Lz,WT/Lb=4.4) provides nominally two-dimensional flow for more than half of the spanwise extent of the test section. Analysis in the streamwise/wall-normal plane along the center of the test section shows low-frequency (St<0.1) large-scale motion of the separated region. The flowfield contains features of both geometry-induced and pressure-gradient-induced separation, but unsteady dynamics produce dominant frequencies closer to geometry-induced TSBs (St≈0.1) compared to purely pressure-gradient-induced TSBs (St≈0.01). Measurements along the spanwise direction and parallel to the initial shear layer development show strong evidence that the low-frequency motion is inherently three-dimensional, providing an additional dimension to the understanding of the flapping/breathing typically observed in planar streamwise/wall-normal measurements. Spectral proper orthogonal decomposition and low-order modeling identify spanwise undulations with wavelengths of the order of Lb and frequencies of St<0.1. The three-dimensional behavior causes a peak/valley formation along the span and a more localized expansion/contraction, leading to only small variations in the integral volume of the TSB.

Two-dimensional spanwise flow regime influenced by tip vortex around a ground-mounted square cylinder in low turbulence uniform flow

The time series data of the lift force acting on a ground-mounted square cylinder in low-turbulence uniform flow reveal a distinctive pattern characterized by a predominant high-amplitude process modulated by intermittent low-amplitude fluctuations. This behavior arises from the intricate interplay between tip and Kármán vortices. However, conflicting interpretations persist, with some findings even presenting contradictory conclusions, particularly regarding the presence of symmetric shedding in the fluctuating lift force process with low amplitude. Furthermore, a clear consensus regarding the mechanism governing the interaction between the tip vortex and the spanwise vortex remains elusive. This study aims to elucidate the two-dimensional flow regime in the spanwise direction influenced by the tip vortex of a ground-mounted square cylinder in low-turbulence uniform flow through experimental investigation. Multiple-point synchronous pressure measurement and particle image velocimetry systems are utilized to measure wind pressure on the side walls and the corresponding flow field at 2/3 of the cylinder's height. The analysis confirms the presence of two distinct types of lift force coefficient behavior: low-amplitude fluctuation (LAF) characterized by longer durations and high-amplitude fluctuation (HAF) occurring in shorter intervals. Subsequently, the flow regime in the near wake corresponding to each mode of the lift force coefficient is discussed. It is observed that the LAF regime corresponds to symmetrical vortex shedding with a prolonged shear layer, maintaining nearly constant curvature. Conversely, for HAF, a pronounced Kármán vortex street is evident. This study conclusively demonstrates the existence of symmetrical vortex shedding, which predominantly contributes to the LAF component of the lift force.

Vortex-shedding modes of a pair of side-by-side thin pitching plates

We have conducted three-dimensional (3D) direct numerical simulations to analyze vortex-shedding modes past vertically arranged, side-by-side 3D pitching plates, considering cases where the plates are in the same, opposite, and different phases. The simulations are performed at a Reynolds number Re=1000, with a dimensionless pitching frequency St=1, and a maximum pitching angle θmax=15°. The vortex-shedding modes reveal horseshoe vortices transforming into distorted hairpin-like structures in the far wake for in-phase plates. Opposite phase plates exhibit helical distortion and core bifurcation, while different phase angles produce meridionally twisted, entangled hairpins. We observe a reverse von Kármán vortex street for in- and different-phase plates, while the opposite shows a reverse Kármán vortex street for the upper plate and a Kármán vortex street for the lower plate. The streakline visualizations reveal wake compression and spoke-like structures symmetrically emanating from the shear layer extremities around the plates' central region. We find leapfrog-like cross-stream vortex interaction when the plates are in phase. The line-time diagram reveals alternating patches of low-intensity cells, switching between negative and positive, alongside continuous bands of both positive and negative cells. Both plates produce similar thrust for the parameters examined in this study.

Synchronization under saturable nonlinearity.

In this theoretical work, we introduce a nonlinear gain saturation law representative of the experimentally observed properties manifested by phenomena ranging from aeroacoustic shear layers in self-sustained cavity oscillations to flame heat release rate in thermoacoustic instabilities. Furthermore, this type of saturable gain may be relevant for a wider class of physical systems, such as active laser media in photonics. The nonlinearity discussed herein governs the fullscale behavior of a self-oscillator exhibiting linear loss under large amplitude perturbations, in contrast to the cubic damping and linear gain of the Van der Pol model. A distinctive characteristic of the proposed equation is the simple, well behaved gain term in the slow timescale dynamics.

High-thermal free vibration analysis of functionally graded microplates using a new finite element formulation based on TSDT and MSCT

Recent advancements in additive manufacturing (AM) have revolutionized the design and production of complex engineering microstructures. Despite these advancements, their mathematical modeling and computational analysis remain significant challenges. This research aims to develop an effective computational method for analyzing the free vibration of functionally graded (FG) microplates under high temperatures while resting on a Pasternak foundation (PF). This formulation leverages a new third-order shear deformation theory (new TSDT) for improved accuracy without requiring shear correction factors. Additionally, the modified couple stress theory (MCST) is incorporated to account for size-dependent effects in microplates. The PF is characterized by two parameters including spring stiffness () and shear layer stiffness (). To validate the proposed method, the results obtained are compared with those of the existing literature. Furthermore, numerical examples explore the influence of various factors on the high-temperature free vibration of FG microplates. These factors include the length scale parameter (), geometric dimensions, material properties, and the presence of the elastic foundation. The findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments. In addition, the findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments. In addition, the results of this research will have great potential in military and defense applications such as components of submarines, fighter aircraft, and missiles.

Mean-flow structures of the turbulent boundary layers bounding a two-dimensional separation bubble

Understanding the mean-flow structures of a separated turbulent boundary layer (TBL) is crucial for turbulence modeling. This study investigates the spatial scaling properties of the total shear stress and mixing length in the TBLs bounding a two-dimensional (2D) separation bubble, aiming to derive analytical descriptions for the entire mean-velocity profiles of the TBLs. For the adverse pressure gradient (APG) TBL upstream of the separation bubble, the total shear stress possesses a two-layer structure with an inner layer adhering to a linear law and an outer layer conforming to a defect power law. In contrast, the mixing length profile consists of four layers, namely the viscous sublayer, the buffer layer, the overlap layer, and the wake region. Each of the layers exhibits a power law or a defect power law relationship with the spatial coordinate normal to the wall. In the four-layer structure, three parameters are sensitive to the variation of the APG: the buffer-layer thickness, the relative magnitude of the mixing length at the boundary layer edge, and a defect power law exponent quantifying the extent of the wake region. For the reattached TBL downstream of the separation bubble, the total shear stress consists of two parts. One part is induced by the pressure gradient and retains the two-layer structure, while the other, engendered by the intense turbulence advected from the separated shear layer, exhibits a dual-power-law distribution. The advected turbulence also significantly alters the four-layer structure of the mixing length, resulting in an augmented buffer layer, a diminished overlap layer, and a wake region that mimics a turbulent mixing layer. Via a dilation ansatz to describe the scaling transition between adjacent layers, the study formulates the complete profiles of the total shear stress and mixing length. The formulation leads to the derivation of novel analytical expressions for the entire mean-velocity profiles of the TBLs. The expressions are in precise accord with the direct numerical simulations of an incompressible 2D separation-bubble flow and a 2D impinging shock wave/TBL interaction. The elucidation of the mean-flow structures through this study is anticipated to facilitate the analysis of turbulence models, thereby enhancing their performance in simulating separated TBLs. The construction of the mean-flow descriptions by inspecting the spatial scaling properties of turbulence paves a promising way for theoretical exploration of complex nonequilibrium TBLs.

The effect of swirling injector geometry on the flow dynamics of precessing vortex core

Precessing vortex core (PVC), a typical vortex structure, universally exists in swirling flow fields and originates from the Kelvin–Helmholtz instability of the swirling shear layer. In the combustion chamber, pressure pulsations from PVC might resonantly couple with acoustic modes, leading to thermoacoustic oscillations which is a significant challenge in the development of rocket engines and gas turbines. The present work focuses on the time-averaged and unsteady flow characteristics of different swirling flow fields in the premixed swirling combustor. The PVC observed in the swirlers adopted presents a single helical structure and the PVC frequency is proportional to the incoming flow velocity. Moreover, another low-frequency helical mode located in the downstream region of the flow fields has been identified and categorized as PVC type II to be distinguished with common PVC mode in this study, which originates from the precession of the central recirculation zone. The experimental results further emphasize the effects of the swirling injector geometry on PVC and the low-frequency helical modes. This indicates that as the diameter of the bluff body or the divergence cup angle increases, the energy of the PVC mode decreases while that of the helical mode increases significantly. In addition, the PVC mode would be gradually suppressed as the tail size of the bluff body increases. These results, especially the coexistence of the PVC mode and the low-frequency helical mode, are rarely reported in previous studies, and they may provide an effective guidance for investigating the mechanism and control of thermoacoustic oscillations.

An experimental study of thermoacoustic instabilities in a RP-3 fueled multi-swirl stabilized lean direct injection combustor

An investigation of self-excited combustion instabilities in a RP-3 fueled, multi-swirl stabilized, lean direct injection (LDI) combustor was performed and investigated with different operating conditions (inlet Reynolds number and fuel–air ratio (FAR)). Pressure fluctuation and heat release data were simultaneously collected using a 3-channel synchronous acquisition system. The results show that as the FAR increases, combustion transitions from a low oscillation mode to a high oscillation mode. During the modal transition, the oscillating flame structure, formed by vortex shedding in the shear layer and the recirculation zone, is then transformed into contraction and expansion movements from the front of the central recirculation zone towards the downstream and radial directions of the combustor. When combustion is in a low oscillation mode, the driving capability of the flame is relatively low. Upon entering a high oscillation mode, the overall driving energy of the flame can maintain combustion in a limit cycle oscillation state.