Shedding Process Research Articles

Verification and validation of Large Eddy Simulation of attached cavitating flow around a Clark-Y hydrofoil

This study uses implicitly filtered Large Eddy Simulation with a homogenous cavitation model to investigate the transient turbulent cavitating flow around a Clark-Y hydrofoil with emphasis on Verification and Validation (V&V). The numerical results indicate that the present simulation can predict the time evolution process of the periodic cavity shedding and agree reasonably with the available experimental data. This study presents the first practical application of LES V&V in a transient cavitating flow. The three-equation method is used to assess the LES error magnitudes in unsteady cavitating flow. The results show that a noticeable difference can be observed between the modeling error and numerical error, and the former has a larger magnitude than the latter in cavitating flow. It is demonstrated that the unsteady cavitation has a big impact on the LES errors. Additionally, compared with non-cavitating flow, the unsteady cavitation increases the values and fluctuation amplitudes of numerical, modeling, and total errors. Grid requirement for modeling the cavitating flow has been discussed from the viewpoint of LES V&V. The numerical results also reveal that the periodic cavity shedding causes the complex and turbulent flow feature by vortex and spectrum analyses, and this has a great influence on the simulation accuracy.

Unsteady dynamic analysis for the cavitating hydrofoils based on OpenFOAM

Recently, cavitation has attracted great attention not only due to its negative effect on the performance of fluid machinery, but also owing to its vigorous prospect in drag reduction for underwater vehicles. However, strong instability and obvious nonlinearity exist for cavitating flow, making it hard to predict it precisely. In this paper, a cavitating solver coupled with the Bubble-Droplet cavitation model has been established based on the OpenFOAM platform. Simulation has been carried out for the cavitating hydrofoil of Clark-Y. Transient evolutions of the flow parameters including the void fraction, velocity, and pressure have been obtained, giving detail insights on the unstable shedding dynamics for the cavitating hydrofoil. Evaluation of the Bubble-Droplet cavitation model has been implemented by varying the threshold value in the model. The transient cavity shape, shedding frequency, and time-dependent curves for the hydrodynamic coefficient have been carefully compared, indicating that this threshold value has obvious effect on the cavity profile during the shedding process. By comparing with the experimental data, the predicted lifts are slightly under-predicted while the drags are over-predicted, but basically the numerical results agree with the experiment well.

Development of a multiphase cavitation solver and its application for ventilated cavitating flows with natural cavitation

The aim of this article is to develop a cavitation solver capable of dealing with the cavitating flow where more than three phases coexist based on the OpenFOAM platform. A new phase change class coupled with newly reported cavitation models and turbulence models has been implemented in the solver. Firstly, validations have been carried out using cases of a two-dimensional cavitating hydrofoil and a three-dimensional projectile near the free surface. The pressure distribution and the gas-liquid interface profile agree well with the experimental data. The solver is then applied for a base-ventilated cavitating hydrofoil with different angle of attack where natural cavitation could occur simultaneously on the hydrofoil surface. The cavity shape as well as the transient cavity shedding process are correctly predicted using the PANS turbulence model. The resulting velocity and pressure distributions are clearly analyzed, giving great insights into the formation and deformation mechanisms of the ventilated cavity. The developed solver is proved to be accurate and efficient in solving the details of turbulent multiphase flows with phase change occurring and has great potential for future applications.

Multimodal partial cavity shedding on a two-dimensional hydrofoil and its relation to the presence of bubbly shocks

The shedding dynamics of partial cavitation forming on a NACA0015 hydrofoil is known from the previous studies to be multimodal, exhibiting abrupt changes in Strouhal number as the cavitation number is reduced (Arndt et al. in Instability of partial cavitation: a numerical/experimental approach. National Academies Press, Washington, D.C., Retrieved from the University of Minnesota Digital Conservancy. http://hdl.handle.net/11299/49781 , 2000). The present study aims to understand the underlying shedding mechanisms responsible for this abrupt change in dynamics. As was observed in Ganesh et al. (J Fluid Mech 802:37–78, 2016), the shedding process can result from both re-entrant liquid flow and the formation of propagating bubbly shock waves within the cavity. Time-resolved X-ray densitometry and high-speed videography are combined with time synchronous measurements of acoustic noise produced by the cavity to examine the formation and shedding of the partial cavitation on a NACA0015 hydrofoil. From the experiments on the hydrofoil, it was observed that the mean cavity length increased with decreasing cavitation number, as expected. At higher pressures, stable partial cavities formed that shed smaller vapor clouds mainly due to the re-entrant liquid flow in the cavity closure. With a reduction in cavitation number, the partial cavity grew in length, and shedding often occurred when the cavity was pinched-off from its leading edge. Once a large region of vapor was shed, the pressure pulse caused by its subsequent collapse could suppress the growth of the newly forming partial cavity. This feedback led to complex, multistep cavity shedding dynamics. At still lower cavitation numbers, bubbly shocks were found to be responsible for the strongest periodic shedding of vapor clouds. Spectral analysis of the acoustic signal revealed a multimodal nature, which was more pronounced at lower cavitation numbers, and similar dynamic behavior was also found for the time varying local void fraction measurements in the vicinity of cavity closure. The occurrence of strongest multimodal behavior was also characterized by the presence of bubbly shock waves as the dominant mechanism of shedding. From the measurements and analysis, it is concluded that at least four different types of shedding modes occurred over a range of cavitation numbers at a fixed attack angle (10°).

Wake structures and acoustic resonance excitation of a single finned cylinder in cross-flow

This paper presents an experimental and numerical investigation to clarify the effect of circular fins on the wake structures, the dynamic loading, as well as the flow–sound interaction mechanism downstream of a single finned cylinder in cross-flow. It is revealed that adding circular fins to the cylinder enhances the flow coherence along the cylinder’s span, strengthens the intensity of the vortex shedding process downstream of the cylinder, reduces the vortex formation length, and increases the dynamic lift force acting on the cylinder. Thus, adding circular fins to the cylinder makes the flow more susceptible to acoustic resonance excitation, compared to an equivalent bare cylinder. Three-dimensional numerical simulations of the flow field around the cylinder show that the flow is entrained between the fins which results in the generation of an accelerated jet-like flow in the developing shear layer region. The jet-like flow emanating from the fins leads to a closer and stronger shear layer roll-up, and hence a shorter vortex formation region. This, in turn, increases the fluctuating lift force on the cylinder, as the strong oscillating shear layers occur closer to base of the cylinder. Additionally, with the reduction of the vortex formation length, the base pressure coefficient decreases and therefore the drag force on the cylinder increases. These intrinsic flow features explain the global effect of circular fins on the vortex shedding process and there by on the excitation mechanism of acoustic resonance.

Vortex formation and evolution for flow over a circular cylinder excited by symmetric synthetic jets

The flow around a circular cylinder is controlled by a pair of synthetic jets symmetrically positioned near the separation points at a Reynolds number of 1200. The flow field in the near wake is measured by a collaboration of the flow visualization and the particle image velocimetry (PIV) techniques. The experiment is conducted under six different momentum coefficients Cμ, ranging from 0.007 to 0.421, while seven excitation frequencies are selected as harmonics of the dominant frequency. Various wake patterns appeared during this study, among which are the 2S asymmetric mode, the 2(P + S) asymmetric mode, the 2P symmetric mode, the 2S symmetric mode and the bistable state where vortices shed with both symmetric and asymmetric modes. The phase averaging method, the proper orthogonal decomposition (POD) based vorticity reconstruction and Fourier analysis are adopted to study the vortex dynamics. Particular attention is given to the vortex-formation mechanism for different modes under Cμ = 0.187, when all of the typical modes emerged. Vortex behaviors under symmetric excitation can be interpreted by looking into the processes of flow separation and vortex shedding. It is shown that synthetic jets can lead to unsteady flow separation and various vortex shedding modes are influenced by the periodic vorticity concertation induced by the synthetic jets.

Relationship between bubble characteristics and hydrodynamic parameters for single bubbles in presence of surface active agents

Rising single air bubbles were investigated in aqueous solutions of hexadecylamine (HDA) and methyl isobutyl carbinol (MIBC) as surface active agents at varying concentrations at a constant gas flow rate. Shadowgraphy was applied to determine main bubble characteristics, such as equivalent diameter, morphology, and rising velocity. From these characteristics, critical parameters like the concentration at the minimum bubble velocity were derived. Simultaneous application of Particle Image Velocimetry (PIV) provided information about hydrodynamic parameters, e.g. the induced liquid velocities and vortex shedding.From surface tension measurements, the concentration of adsorbed species on the interface and packing densities of HDA and MIBC on the bubble surface could be calculated. HDA exhibited a better adsorption and a higher packing density on the bubble surface compared to MIBC due to the ionic character and the straight hydrocarbon chain. The bubble characteristics were therefore more strongly affected by HDA than by MIBC.Combining the Shadowgraphy and PIV results it was found that the mean liquid velocity as well as the amount of induced turbulent kinetic energy increased with increasing concentration of surfactants in the solutions, while the investigated bubble characteristics such as equivalent diameter and rising velocity decreased. The increase in mean liquid velocity and induced turbulent kinetic energy could be correlated with the oscillating frequency of the bubble trajectory, which also increased with increasing surfactant concentration. The vortex shedding process could be visualised using Proper Orthogonal Decomposition (POD) revealing the micro-process of energy cascading.

Effect of water temperature and fish biomass on environmental DNA shedding, degradation, and size distribution.

Environmental DNA (eDNA) analysis has successfully detected organisms in various aquatic environments. However, there is little basic information on eDNA, including the eDNA shedding and degradation processes. This study focused on water temperature and fish biomass and showed that eDNA shedding, degradation, and size distribution varied depending on water temperature and fish biomass. The tank experiments consisted of four temperature levels and three fish biomass levels. The total eDNA and size‐fractioned eDNA from Japanese Jack Mackerels (Trachurus japonicus) were quantified before and after removing the fish. The results showed that the eDNA shedding rate increased at higher water temperature and larger fish biomass, and the eDNA decay rate also increased at higher temperature and fish biomass. In addition, the small‐sized eDNA fractions were proportionally larger at higher temperatures, and these proportions varied among fish biomass. After removing the fish from the tanks, the percentage of eDNA temporally decreased when the eDNA size fraction was >10 µm, while the smaller size fractions increased. These results have the potential to make the use of eDNA analysis more widespread in the future.

Experimental and numerical investigation of cavitating vortical patterns around a Tulin hydrofoil

The objective of this paper is to investigate the cavitating flow patterns around a specific hydrofoil (Tulin hydrofoil) via combined experimental and numerical studies, and to better understand the vortex-cavitation interactions in transient cavitating flows. The experimental studies were carried out in the closed-loop cavitation tunnel, and a high-speed digital camera is applied to document the cavitation patterns. The numerical investigations are performed using a large-eddy simulation method and the Zwart cavitation model. The results showed that the predicted cavity formation and evolution agree well with the experimental observation. With decreasing of the cavitation number, different cavitating flow patterns occur around the hydrofoil, namely inception cavitation (σ = 1.57), vortex cavitation (σ = 1.27), cavitating vortex street (σ = 1.07), cloud cavitation (σ = 0.87), mixture supercavitation (σ = 0.67), and developed supercavitation (σ = 0.54). Especially, the flow structures of vortex cavitation, cavitating vortex street and cloud cavitation were further investigated with the Euler and Lagrangian method. For vortex cavitation, the cavitating vortex forms and sheds at the leading and trailing edge of the foil alternatively, with a pair of asymmetric vortex structures observed. The trailing edge cavitating vortex has a regular vortex shape and a clear boundary between the vortex structures. For cavitating vortex street, vortex shedding process is not independent, instead, the vortex braid between the trailing edge cavitating vortexes and the so called “cat's eye” vortex row can be obviously observed. The center of circulation region is corresponding to low finite-time Lyapunov exponent (FTLE) value, and the bridges of the FTLE is concentrated in the boundary of the vortex structure and curling in the dynamic surrounding of the circulation region. The trajectory of the points well presents the dynamic flow pattern. For cloud cavitation pattern, the cavity develops to cover the entire suction surface, and the cloud cavity sheds downstream periodically.

Active control of circular cylinder flow with windward suction and leeward blowing

This study is an experimental investigation of the effectiveness and mechanism of a concept for bluff-body control characterized by combined windward suction and leeward blowing (WSLB). Wind tunnel tests are performed at a subcritical Reynolds number (Re) of 3.33 × 104. Open-loop WSLB is used to control the flow around a cylindrical test model. Distributed suction and blowing nozzles are symmetrically arranged at the front and rear stagnation points. Steady suction and blowing are implemented simultaneously on both surfaces of the cylinder. WSLB control is characterized by the dimensionless momentum of the suction/blowing relative to the incoming airflow. Instantaneous pressure distributions on the midspan of the cylinder surface for the baseline and controlled cases are measured to quantify the modifications of WSLB control to the aerodynamic coefficients of the cylinder. In addition to surface pressure measurements, a particle image velocimetry (PIV) system is used to describe the wake flow structures of the baseline and controlled cylinders. Experimental results demonstrate that WSLB control decreases sectional drag at the midspan and reduces the fluctuating amplitudes of dynamic wind loads acting on the cylinder. The Strouhal number to characterize the vortex shedding frequencies of the controlled cylinders is also found to deviate from that of the natural cylinder. PIV measurement results show that the active blowing positioned at the leeward stagnation point forms a pair of vortices into the cylinder wake that modify the original vortex shedding process. As the blowing vortices convect into the wake, they stretch the unsteady shear flows from the upper and lower sides of the cylinder, increase the vortex-formation length and push the alternative vortex shedding further downstream. It is also shown that a steady and symmetric perturbation imposed on the periodic cylinder flow can reduce the von Karman vortices and modify the mode of wake vortex shedding significantly. With active control of windward suction and leeward blowing (WSLB), blowing positioned at the leeward stagnation point forms a pair of vortices in the cylindrical wake that modifies the typical vortex shedding process. As the blowing vortices convect downstream, they contribute to detaching the unsteady shear layers from the cylinder. It is shown that a steady and symmetric perturbation imposed on the periodic cylinder flow can lead to a symmetric mode of wake vortex shedding.

Numerical Investigation of the Effects of Nonsinusoidal Motion Trajectory on the Propulsion Mechanisms of a Flapping Airfoil

The effect of nonsinusoidal trajectory on the propulsive performances and the vortex shedding process behind a flapping airfoil is investigated in this study. A movement of a rigid NACA0012 airfoil undergoing a combined heaving and pitching motions at low Reynolds number (Re = 11,000) is considered. An elliptic function with an adjustable parameter S (flattening parameter) is used to realize various nonsinusoidal trajectories of both motions. The two-dimensional (2D) unsteady and incompressible Navier–Stokes equation governing the flow over the flapping airfoil are resolved using the commercial software starccm+. It is shown that the nonsinusoidal flapping motion has a major effect on the propulsive performances of the flapping airfoil. Although the maximum propulsive efficiency is always achievable with sinusoidal trajectories, nonsinusoidal trajectories are found to considerably improve performance: a 110% increase of the thrust force was obtained in the best studied case. This improvement is mainly related to the modification of the heaving motion, more specifically the increase of the heaving speed at maximum pitching angle of the foil. The analysis of the flow vorticity and wake structure also enables to explain the drop of the propulsive efficiency for nonsinusoidal trajectories.

Two-dimensionalization of a three-dimensional bluff body wake

The three-dimensional flow characteristics of a circular cylinder with synthetic jet control are numerically studied using large eddy simulation. The Reynolds number based on the diameter of the cylinder is Re = 500. The control effects and underlying mechanism are revealed to show how the synthetic jet changes the three-dimensional wake pattern. Analysis of the dynamic control process indicates that the blowing stroke helps the shear layer to assemble vorticity, and then, the suction stroke accelerates the detachment of the concentrated vorticity. The vortex shedding process will be gradually dominated by symmetric actuation of the synthetic jets. Thus, the asymmetric vortex shedding mode could be changed into a symmetric mode several periods after actuation at certain excitation frequencies, leading to significant suppression of lift fluctuations. A periodic pressure variation at the leeward surface of the circular cylinder caused by the changes of the separation point for the flow over a circular cylinder and recirculation region results in a large drag fluctuation. The excitation phase influences only the control process, but not the final state, while the excitation frequency plays an important role in the formation of different wake patterns. It is also found that the synthetic jet can completely suppress the formation of streamwise vortices due to the three-dimensional instability suppression and reduce the deformation of spanwise vortices, resulting in a conversion of the original three-dimensional flow into a two-dimensional one. Such two-dimensionalization can be achieved for both asymmetric and symmetric wake patterns, indicating that it is not influenced by the excitation phase and frequency as long as the actuation is two-dimensional.

Experimental investigation of liquid nitrogen cavitating flows in converging-diverging nozzle with special emphasis on thermal transition

The objective of this paper is to investigate the dynamic evolution of unsteady liquid nitrogen cavitating flows in a wide range of free-stream conditions and propose a thermal parameter to evaluate and predict the transition process of two typical cavitation dynamics in liquid nitrogen. The dynamic evolutions of liquid nitrogen cavitating flows in a converging–diverging (C-D) nozzle with a throat height of 2.0 mm under a wide range of free-stream conditions were experimentally investigated. Experiments were carried out in liquid nitrogen with the temperature range from 68 K to 86 K, the pressure in the tanks is within the range of 30–300 kPa. The results show that two typical cavitation dynamics, namely the quasi-isothermal mode and the thermo-sensitive mode were observed under similar cavitation number and Reynolds number with the increasing throat temperature. The cavitation dynamics transits from the quasi-isothermal mode to the thermo-sensitive mode with the increasing throat temperature, and the transition temperature (transition mode) is approximately at 77–78 K. In the quasi-isothermal mode, the shedding cavity with clear interface collapses immediately after shedding. The cavity area increases with the increasing temperature under similar cavitation number and Reynolds number. In the transition mode, the magnitude of cavity area, the time duration of the shedding process, as well as the cavitation aggressiveness reaches the maximum values. In the thermo-sensitive mode, the shedding cavity turns to be mushy and frothy, and the mushy interface collapses slowly after shedding. The cavity area decreases with the increasing temperature under similar cavitation number and Reynolds number. When the thermodynamic effects completely dominate the change of the cavitation dynamics in the thermo-sensitive mode, the cavitation process becomes more stable. The shedding cavity collapses more slowly, while moves more quickly. The thermal parameter C-factor could quantitatively evaluate and predict dynamics transition from the quasi-isothermal mode to the thermo-sensitive mode in liquid nitrogen cavitating flows. The transition mode (transition temperature) should be prevented from causing the maximum cavitation aggressiveness in liquid nitrogen apparatus or system.

Wake control using spanwise-varying vortex generators on bridge decks: A computational study

A passive control device called spanwise-varying vortex generator (VG) is proposed to mitigate vortex shedding of a bridge model, since the 3D spanwise-varying control method shows high efficiency in suppressing vortex shedding behind bluff bodies. Pairs of VGs were arranged on the lower surface of the bridge in the spanwise direction to generate streamwise vortices and perturb two-dimensional spanwise vortex shedding. Delayed detached-eddy simulation and dynamic mode decomposition were carried out to examine their effects on wake control. The results demonstrate that with VG control, the regular spanwise vortices are highly distorted and are accompanied by a spanwise mismatch in the vortex shedding process. Consequently, the regular spanwise vortex shedding is substantially suppressed, resulting in a considerable reduction in vortical strength in the wake and significant increases in the vortex formation length. In addition, the dynamic mode decomposition reveals that VGs can redistribute the energy spectrum and transport the energy from the mode associated with the regular vortex shedding to other low-frequency modes. Therefore, forces induced by vortex shedding are considerably reduced.

New method for warp yarn arrangement and algorithm for pattern conversion for three-dimensional woven multilayered fabrics

Three-dimensional fabrics have an enormous potential for the manufacturing of semi-finished products in a direct preforming procedure for fiber-reinforced materials. The production of these three-dimensional fabrics involves the processing of coarse reinforcing yarns with high warp density. However, conventional weaving looms have not been designed for such applications, and their maximal achievable warp yarn density is therefore severely limited. Friction and clamping between warp yarns impede the shedding process, and fragments of damaged or fibrillated fibers interfere with the weaving process. Most of the solutions for these issues, which has been presented so far, are based on noncommercial technologies or require extensive modification on standard weaving machines. Hence this paper proposes a new shedding method based on double flat steel heddles, which is suitable for the use in conventional weaving looms. The paper gives a detailed description of the new shedding method including the required materials and the technological framework. Furthermore, a suitable algorithm for the fast pattern conversion under consideration of the special technological framework and requirements of the shedding is presented.

Passive noise control technique for suppressing acoustic resonance excitation of spirally finned cylinders in cross-flow

This paper presents an innovative passive noise control technique for suppressing flow-excited acoustic resonance of spirally finned cylinders in cross-flow. This was achieved by maintaining the number of fins, but varying the fin density along the finned cylinder’s span to create a non-uniform finned cylinder. Two non-uniform finned cylinders were investigated with pitch ratios of p(mid)/p(side) = 0.5 and 1.7. To better understand the influence of the non-uniform finned cylinders on the wake structure, bare cylinders with the same effective diameter were investigated. In the non-uniform finned cylinder case, due to the variation in the fin density, the effective diameter along its span changes. Thus, the effective diameter of a non-uniform finned cylinder happens to be a dual diameter cylinder. Three dual diameter cylinders were investigated with diameter ratios ranging between 0.5 ≤ D(mid)/D(side) ≤ 2. These diameter ratios closely correspond to the pitch ratio (p(mid)/p(side)) and effective diameter ratio (Dc(mid)/Dc(side)) of the non-uniform finned cylinders investigated. The results show that the non-uniform finned cylinderscause spatial variations in the vortex shedding process due to dissimilarities in the flow behavior at different fin density regions. Temporal variations were also revealed due to changes in the vortex shedding frequency at different spanwise regions. This resulted in a significant decrease in the spanwise flow coherence and vortex shedding strength. The spatio-temporal variations in the shed vortices at different spanwise regions observed by the non-uniform finned cylinders were found to be analogous to dual diameter cylinders with diameter ratios equivalent to the pitch ratios of the non-uniform finned cylinder. As a result, substantial attenuation in the acoustic pressure during flow-excited acoustic resonance was achieved by the non-uniform finned cylinders. The results presented in this paper show that non-uniform finned cylinders are a viable noise control technique for suppressing flow-excited acoustic resonance in tube bundles of heat exchangers.

Fruitlet shedding is affected by the position in the apple cluster

In apple trees, natural fruitlet shedding is often insufficient to achieve optimal fruit size and yields. Natural fruitlet abscission can be stimulated by several technological measures and its knowledge is crucial for the implementation of adequate measures. The natural phenomenon of fruitlet shedding was monitored in apple trees in two consecutive years. Abscission started 4 weeks after full bloom and lasted for 6 weeks. During this time, more than 70% of all fruitlets shed in one or more peaks, depending on the year. The ‘Golden Delicious’ cultivar predominantly developed clusters with 5 flowers (39%), followed by clusters with 4 flowers (34%) and 6 flowers (24%); clusters with three or seven flowers were rare. Each flower/fruitlet position in the cluster was separately monitored and the link between specific position and abscission was determined. Fruitlets rarely abscised from the central position (less than 40% incidence), while the lowest positions (positions 5 and 6) shed more than 70% of fruitlets. Interestingly, high abscission potential was also observed at the 2nd position (nearest to the central position), from which fruitlets abscised more frequently than from lower positions. Results confirm at least partly the carbohydrate theory of apple fruitlet shedding and describe the shedding process as a type of stress. However, sugar and/or phenolic contents are not the only reasons for the initiation of the shedding process.

Decentralized Load Shedding Method Based on Voltage Stability Margin Index Using Synchrophasor Measurement Technology

This study develops an analytical method for assessing the voltage stability margins of a decentralized load shedding scheme; it then examines the challenges related to the existing load shedding scheme. It also presents a practical application for implementing the proposed method, based on the synchrophasor measurement technology in modern power grid operations. By applying the concept of a continuously-computed voltage stability margin index to the configuration of the Thévenin equivalent system, the maximum transfer power could be used as an index to monitor the voltage instability phenomenon and thus determine the required load shedding amount. Thus, the calculated voltage stability margin might be a useful index for system operators in the critical decision-making process of load shedding. Dynamic simulations are performed on real Korean power systems as case studies. Simulation results, when comparing the existing and proposed methods, showed that there was a considerable reduction in the amount of load shedding in the voltage instability scenario. This indicates that the synchrophasor measurement technology has a considerable effect on the proposed load shedding method. The simulation results have validated the performance of the proposed method.

Asymmetric characteristics of the shock bifurcation in the reflected shock/boundary layer interaction

PurposeWhen a reflected shock interacts with the boundary layer in a shock tube, the shock bifurcation occurs near the walls. Although the study of the shock bifurcation has been carried out by many researchers for several decades, little attention has been devoted to investigate the instability pattern of the bifurcation. This research work aims to successfully capture the asymmetry of the whole flow field, and attempt to achieve the instability mechanism of the shock bifurcation by a direct numerical simulation of the reflected shock wave/boundary layer interaction at Ma = 1.9. In addition, the reason for the formation of the bifurcated structure is also explored.Design/methodology/approachThe spatial and temporal evolution of the shock bifurcation is obtained by solving the two-dimensional compressible Navier–Stokes equations using a seventh-order accurate weighted essentially non-oscillatory (WENO) scheme and a three-step Runge–Kutta time advancing approach.FindingsThe results show that the formation of shock bifurcation is mainly because of the shock/gradient field interaction, and the height of the bifurcated foot increases with the growth of the shock intensity and the gradient field. The unsteady asymmetry of the upper and bottom shock bifurcated structures is because of the vortex shedding with high frequency in the rear recirculation zone, which leads to the fluctuation of the recirculation area. The vortex shedding process behind the bifurcated structure closely resembles the Karman vortex street formed by the flow around the cylinder. The dimensionless vortex shedding frequency varies between 0.01 and 0.02. In comparison to the scenario at Ma = 1.9, the occurring time of instability is delayed and the upper and bottom bifurcated feet intersect in a relatively short time at Ma = 3.5. The region behind the bifurcated shock is a transitional flow field containing obvious cell structures and “isolated islands.”Originality/valueThis paper discovers an unsteady flow pattern of the shock bifurcation, and the mechanism of this instability in the reflected shock/boundary layer interaction is revealed in detail.

Proper orthogonal decomposition analysis of boundary layer oscillating aspiration controlling separation flows in two-dimensional compressor cascades

Vortex structures of the separation flow fields in two-dimensional compressor cascades controlled by the boundary layer oscillating suction are numerically investigated. The proper orthogonal decomposition method is adopted to present the variation of characteristics owned by large-scale vortices. It is found that introducing unsteady excitations with proper frequencies into the steady aspiration results in a more effective control effect and the optimal oscillation frequency should be in line with the characteristic frequencies of the steady aspirated flow field. The separation flows can be decomposed in to several basic structures with the dominant one being in the manner of Karman vortex street regardless of the control method adopted. The boundary layer oscillating suction not only alleviates the separation by removing low-energy fluid, but also intensifies the harmonic flow element represented by proper orthogonal decomposition modes with others suppressed. The well-organized vortex shedding process could contribute to the loss reduction to some extent.