Vortex Street Research Articles

Flow and coherent structures generated by a circular array of rigid, emerged cylinders in a shallow channel

The study investigates the flow structure, dynamics of the large-scale coherent structures, drag forces and sediment entrainment mechanisms generated by a circular array of diameter D containing rigid emerged circular cylinders of diameter d placed in a smooth-bed channel of depth h under strong shallow flow conditions (D/h = 20, d/D = 0.0125 and 0.025). Eddy resolving simulations are conducted with different values of the solid volume fraction 0.025 ≤ SVF ≤ 0.1 and non-dimensional frontal area per unit volume (2.56 ≤ aD ≤ 10.2, where for the present configuration, a = SVF(1/d)4/ ${\rm \pi}$ ) and a fixed channel Reynolds number (Reh = 10 000). The flow conditions are such that a vortex street (VS)-type of shallow wake is expected to form for a solid cylinder of diameter D. Findings are compared with previous results obtained for cases with moderately shallow conditions 2.5 ≤ D/h ≤ 3.5 and with the limiting case of flow past a solid cylinder with D/h = 20. For moderately shallow conditions, the core of the main horseshoe vortex (HV) forming around the array occupies a small fraction of the water column and its coherence is the largest in front of the array. By contrast, for very shallow conditions, multiple HVs form around the array and their cores occupy a large fraction of the water column. Moreover, the coherence of most of these HVs peaks close to the sides of the array. Only for relatively large aD values, the main HV extends over the whole upstream face of the array, similar to the limiting case of a solid cylinder. For sufficiently high aD, a secondary instability is present inside the near wake that leads to the formation of parallel horizontal vortices in the vicinity of the wake roller vortices. The changes in the wake structure with decreasing SVF and aD are qualitatively similar to those observed for cases with moderately shallow flow conditions, with the antisymmetric wake shedding mode being suppressed for aD ≤ 2.5. However, the Strouhal number associated with the shedding of wake rollers, which is still close to 0.2 for a solid cylinder with D/h = 20, can be as high as 0.4 for aD = 2.5. The paper also discusses how the steady wake and total wake lengths and the strength of the bleeding flow vary with the SVF. Simulation results show that the capacity of the flow to entrain sediment inside and around the array peaks for SVF = 0.05 and aD = 5.2, with sediment entrainment monotonically increasing with the SVF outside the array and monotonically decreasing inside the array. Despite the differences in the flow structure next to and inside the array, the variation of the mean, time-averaged streamwise drag coefficient of the solid cylinders ${\bar{C}_d}$ with aD is close to that observed for arrays with moderately shallow flow conditions. The combined drag coefficient for the array decreases with increasing flow shallowness, with the decay being stronger for relatively large values of aD.

Triglobal resolvent-analysis-based control of separated flows around low-aspect-ratio wings

We perform direct numerical simulations of actively controlled laminar separated wakes around low-aspect-ratio wings with two primary goals: (i) reducing the size of the separation bubble and (ii) attenuating the wing tip vortex. Instead of preventing separation, we modify the three-dimensional (3-D) dynamics to exploit wake vortices for aerodynamic enhancements. A direct wake modification is considered using optimal harmonic forcing modes from triglobal resolvent analysis. For this study, we consider wings at angles of attack of $14^\circ$ and $22^\circ$ , taper ratios $0.27$ and $1$ , and leading edge sweep angles of $0^\circ$ and $30^\circ$ , at a mean-chord-based Reynolds number of $600$ . The wakes behind these wings exhibit 3-D reversed-flow bubble and large-scale vortical structures. For tapered swept wings, the diversity of wake vortices increases substantially, posing a challenge for flow control. To achieve the first control objective for an untapered unswept wing, root-based actuation at the shedding frequency is introduced to reduce the reversed-flow bubble size by taking advantage of the wake vortices to significantly enhance the aerodynamic performance of the wing. For both untapered and tapered swept wings, root-based actuation modifies the stalled flow, reduces the reversed-flow region and enhances aerodynamic performance by increasing the root contribution to lift. For the goal of controlling the tip vortex, we demonstrate the effectiveness of actuation with high-frequency perturbations near the tip. This study shows how insights from resolvent analysis for unsteady actuation can enable global modification of 3-D separated wakes and achieve improved aerodynamics of wings.

A comprehensive study of recent studies on the efficiency of axial flow turbines with an investigation on blade profile modifications in stator and rotor assemblies

Axial flow turbines are crucial in energy production and propulsion across diverse applications. As global energy needs rise, optimizing turbine efficiency is paramount. This review delves into the aerodynamic design of turbine blades, specifically examining blade profile modifications in both stator and rotor assemblies of state-of-the-art models proposed in the studies from 2019 to 2024. The focus is on mitigating performance discrepancies between idealized simulations and real-world applications, which present significant challenges such as inconsistencies in computational fluid dynamics (CFD) predictions and manufacturing constraints. Key findings from this review highlight a potential efficiency gain of 1%–3% through optimal blade designs that reduce incidence losses, secondary flows, and tip vortex formation. Advanced modeling techniques, including high-fidelity, multi-objective optimization with machine learning, are evolving to better predict and enhance turbine performance. However, gaps remain in system-level integration and the limited experimental data restricts comprehensive validation of these new designs. The insights from this review will aid the research community by identifying critical areas for future investigation, such as integrating blade aerodynamics with heat transfer and structural mechanics. Further, it emphasizes the need for exploring combinations of passive and active flow control strategies to fully harness the benefits of blade profile enhancements. These efforts are crucial for achieving substantial improvements in turbine efficiency, which are essential for meeting the growing demands for sustainable and efficient energy production.

Aerodynamics of a three-dimensionally deformed rigid wing

A flexible wing with a large aspect ratio emerges in many modern engineering applications (e.g. solar planes and super large wind turbine blades) and its interaction with incident flow differs markedly from conventional fluid–structure interactions (FSI), exhibiting frequently a large three-dimensional (3D) deformation. Yet, there is little information on how such deformation may change wing aerodynamics. This work investigates the aerodynamic performance of deformed and cantilever-supported NACA0012 rigid wings with an aspect ratio of 9, using ANSYS Fluent with the SST-κ-ω turbulence model at a chord-length-based Reynolds number Rec of 1.5 × 105. Numerical simulation is validated experimentally. The wing tip bending displacement is up to 4.14c, and the maximum twisted angle is up to 7°. The angle α of attack varies from 0° to 20° at mid span of the wing. It has been found that the torsional deformation can significantly advance the local flow separation, reattachment, bubble length, and transition from laminar to turbulence, resulting in a drop in the critical angle αcr of attack, at which the separation bubble size reaches the maximum. Accordingly, the lift and drag coefficients increase, as well as the bending and pitching-up moments, though the stall is advanced due to a change in local α. The tip vortex is also enhanced, inducing strong downwash postponing the separation bubble on the wing and resulting in redistributed force near the wing tip that increases markedly the local bending moment but decrease the local pitching-up moment. On the other hand, the bending deformation tends to produce an effect opposite to the torsion on the flow structure and causing little change in the lift coefficient, though reducing the induced drag and moments appreciably. With both deformations in place, the torsion overwhelms the bending in general in terms of its impact upon aerodynamics and flow structures, the latter acting to cancel at least partially the effect of the former.

Comparative Performance Assessment between Incompressible and Compressible Solvers to Simulate a Cavitating Wake

To study the effects of fluid compressibility on the dynamics of a cavitating vortex street flow in a regime where the vortex shedding frequency increases as a result of the cavitation increase, the cavitating wake behind a wedge was simulated employing both incompressible and compressible solvers. To do this, a compressible cavitation model was implemented, modifying the Zwart-Gerber-Belamri (ZGB) incompressible solver and including a pressure limit and absorbing boundary conditions to prevent a non-physical pressure field. To validate the performance of the compressible model, preliminary simulations were carried out on a 1D Sod cavitating tube and the cavitating vortex shedding behind a circular body at laminar flow conditions. The results of the cavitating wake behind the wedge with the incompressible and the compressible solvers showed similar predictions in terms of pressure, vortex shedding frequency, and instantaneous and average vapor volume fraction profiles. In spite of this, differences were obtained in the energy content of the fluid force fluctuations on the body at higher frequencies, which appear to be better resolved and amplified when the compressibility model is considered. Overall, both solvers provided comparable results in terms of cavitation phenomena that are well aligned with experimental observations.

Numerical investigation of the effect of winglet configurations with multiple cant angles on the aerodynamic performance of wind turbine blade

ABSTRACT A numerical investigation of the effects of winglets with multiple cant angles on the power output of the blade of a horizontal axis wind turbine (HAWT) is conducted. Several winglet configurations with single and multiple cant angles are designed and their performance is evaluated. Numerical solutions obtained by RANS equations and moving reference frame method were compared with the experiments and demonstrated that they concur well with the experimental data. In the torque and thrust comparison, the ones with multiple cant angles present better power output enhancement than those with a single cant angle at a relatively high wind speed. The configurations of multiple cant angles are effective in reducing the influence of wing tip vortices, resulting in a higher torque while maintaining the same winglet length and height.

Experimental and computational investigations of flexible membrane nano rotors in hover

With reduced size, the flight Reynolds number of the nano rotor decreases, leading to a sharp drop in the aerodynamic efficiency of the nano rotor. Therefore, improving the aerodynamic performance of the nano rotor at low Reynolds numbers through flow control methods becomes imperative. In this study, from the perspective of bionics, flexible materials are employed in nano rotor design. Seven different layouts of flexible membrane rotor blades are designed and fabricated. The influence of leading and trailing edge flexibility, as well as membrane occupancy ratio on rotor blade propulsion characteristics, is explored through propulsion performance tests in hover.Results show that among several layouts proposed in this study, the layout with both reinforced leading and trailing edges of the flexible membrane nano rotor blade exhibits excellent propulsive performance. However, the propulsion performance of the flexible membrane rotors doesn't vary linearly with the ratio of membrane area to the whole rotor area. The appropriate ratio or flexibility can increase the propulsive performance of the rotor, especially at medium and high collective angles. At 7000 RPM and a 20° collective angle, the Figure of Merit of the flexible membrane nano rotor increases up to 4.2% when comparing with the nano rotor without membrane. This improvement becomes more significant with higher collective angles. The structural natural vibration characteristics of each flexible membrane with different layouts are analyzed through modal tests, ensuring the accuracy of the finite element model for flexible membrane rotors. Numerical analysis of the fluid-structure coupling of a flexible membrane rotor with different layouts indicates that rotor structural vibrations is highly consistent with fluctuation of aerodynamic parameters. The deformation of the flexible membrane under aerodynamic forces enhances local blade camber, but reduces angles of attack. This, subsequently, minimizes the size of laminar separation bubbles and the intensity of the blade tip vortices at high collective angles. Consequently, rotor power coefficients decrease, and overall aerodynamic performance improves.

Biomimetic Wings for Micro Air Vehicles.

In this work, micro air vehicles (MAVs) equipped with bio-inspired wings are investigated experimentally in wind tunnel. The starting point is that insects such as dragonflies, butterflies and locusts have wings with rigid tubular elements (corrugation) connected by flexible parts (profiling). So far, it is important to understand the specific aerodynamic effects of corrugation and profiling as applied to conventional wings for the optimization of low-Reynolds-number aerodynamics. The present study, in comparison to previous investigations on the topic, considers whole MAVs rather than isolated wings. A planform with a low aperture-to-chord ratio is employed in order to investigate the interaction between large tip vortices and the flow over the wing surface at large angles of incidence. Comparisons are made by measuring global aerodynamic loads using force balance, specifically drag and lift, and detailed local velocity fields over wing surfaces, by means of particle image velocimetry (PIV). This type of combined global-local investigation allows describing and relating overall MAV performance to detailed high-resolution flow fields. The results indicate that the combination of wing corrugation and profiling gives effective enhancements in performance, around 50%, in comparison to the classical flat-plate configuration. These results are particularly relevant in the framework of low-aspect-ratio MAVs, undergoing beneficial interactions between tip vortices and large-scale separation.

Simulating cross-scale flow dynamics around offshore monopile foundations with a GFD-CFD coupled model

Flow dynamics are complex and undergo significant impact from offshore engineering infrastructures, such as wind turbines, involving interactions across different temporal and spatial scales. Individual numerical models of geophysical fluid dynamics (GFD) or computational fluid dynamics (CFD) face challenges in accurately representing these dynamics. To effectively capture the three-dimensional cross-scale flow around offshore infrastructures, we propose a generalized coupling framework that integrates the unstructured-grid Finite-Volume Community Ocean Model (FVCOM) for GFD and the Open Field Operation and Manipulation (OpenFOAM) for CFD. With the validation against the flume experiment, the common-boundary nesting method was developed to allow an accurate representation of flow dynamics around offshore hydraulic infrastructures. Idealized monopile foundation experiments demonstrate the model's capability to capture the formation of Karman vortex street, rotating horseshoe vortex under realistic astronomical tidal conditions. Application of this coupling framework to the offshore wind farm in Yangjiang, China, reveals flow direction lagging of 15° in the wake of a monopile under diurnal tide. This coupling approach, leveraging the strengths of both CFD and GFD models, provides a universal downscaling methodology in geophysical conditions, for a better understanding of the impact of offshore hydraulic infrastructures on the surrounding environment and further planning offshore engineering projects.

Trigger mechanism for a singing cavitating tip vortex

The discrete tone radiated from tip vortex cavitation (TVC), known as ‘vortex singing’, was recognized in 1989, but its triggering remains unclear for over thirty years. In this study, the desinent cavitation number and viscous correction are applied to describe the dynamics of cavitation bubbles and the dispersion relation of cavity interfacial waves. The wavenumber-frequency spectrum of the cavity radius from the experiment in CSSRC indicates that singing waves predominantly consist of the stationary double helical modes (kθ = 2- and -2+) and the breathing mode (kθ = 0-), rather than standing waves as assumed in previous literatures. Moreover, two trigger mechanisms, expressed by two triggering lines, are proposed: the twisted TVC, initially at rest, is driven into motion through the corrected natural frequency (fn) due to the step change of the far-field pressure. Subsequently, the frequency associated with the zero-group-velocity point (ῶzgv) at kθ = 0- is excited through ῶi, the frequency at the intersection of dispersion curves at kθ = 0- and -2+, or ῶj, the frequency at the intersection of dispersion curves at kθ = 0- and 2-, corresponding to two types of the vortex singing triggering. These solutions, without empirical parameters, are validated using singing conditions provided by CSSRC and G.T.H., respectively. Furthermore, the coherence and the cross-power spectral density spectrum indicates a large-scale breathing wave propagating along the singing cavity surface and travelling from downstream to hydrofoil tip, providing us a comprehensive understanding for the triggering of vortex singing.

Simulation and mechanism analysis of fretting wear of parallel groove clamps in distribution networks caused by Karman vortex vibration

PurposeThe phenomenon of friction and wear in parallel groove clamps under wind vibration in 10 kV distribution networks represents a significant challenge that can lead to their failure. This study aims to elucidate the wear mechanism of parallel groove clamps under wind-induced vibration through simulation and experimentation.Design/methodology/approachFLUENT software was used to simulate the flow around the conductor and the parallel groove fixture, and the Karman vortex street phenomenon was discussed. The stress fluctuations of each component under breeze vibration conditions were investigated using ANSYS, and fretting experimentations were conducted at varying amplitudes.FindingsThe results demonstrate that the impact of breeze vibration on the internal stress of the parallel groove clamps is considerable. The maximum stress observed on the lower clamping block was found to be up to 300 MPa. As wind speed increased, the maximum vibration frequency was observed to reach 72.6 Hz. Concurrently, as the vibration amplitude increased, the damage in the contact zone of the lower clamping block also increased, with the maximum contact resistance reaching 78.0 µO at a vibration amplitude of 1.2 mm. This was accompanied by a shift in the wear mechanism from adhesive wear to oxidative wear and fatigue wear.Originality/valueThis study presents a comprehensive analysis of the fretting wear phenomenon associated with parallel groove clamps under wind vibration. The findings provide a reference basis for the design and protection of parallel groove clamps.

Fluid Dynamics of Interacting Rotor Wake with a Water Surface

Rotor-type cross-media vehicles always induce considerably complex mixed air–water flows when approaching the water surface, resulting in relative thrust loss and structural damage on rotor. The interactions between a water surface and rotor wake bring potential risks to the cross-media process, which is known as the near-water effect of the rotor. In this paper, experimental investigations are used to explore the fluid dynamics of the near-water effect of the rotor. Qualitative droplet observation was carried out on the 0.25 m and 0.56 m diameter commercial rotor blades and the 0.07 m diameter ducted fan near the water surface first to gain a qualitative understanding of droplet characteristics. The results show that the rotor wake caused water surface deformation, droplet tearing off, splashing, and entrainment into the rotor disk. The depression formed by the rotor downwash flow impacting the water surface is named as three modes: dimpling, splashing, and penetrating, and the correlation between the depression modes and the aerodynamic characteristics of the rotor is primary analyzed. The flow mechanisms of dimpling mode were studied using the particle image velocimetry (PIV) technique. The results showed that the cavity and liquid crown obviously alter the flow direction of water surface jets, but not all rotors near water enter the vortex ring state. Two splashing mechanisms were revealed, including the direct ejection of droplets at the rim of depression and the tearing of liquid crown by the water surface jets. The blade tip vortex in the surface jet is a potential cause of entrainment into the rotor disk and secondary breakup of the droplet.

Study on the Influence of Chord Length and Frequency of Hydrofoil Device on the Discharge Characteristics of Floating Matter in Raceway Aquaculture

To investigate the influence of the chord length and frequency of an oscillating hydrofoil device on the discharge characteristics of floating particulate matter, in this study, we take raceway aquaculture as an example and systematically compare and analyze the flow field characteristics of the hydrofoil device with different chord lengths and frequencies, as well as the sewage discharge performance of the raceway based on Computational Fluid Dynamics (CFD). The results indicate that in the particulate matter discharge process of raceway aquaculture, when the chord length and motion frequency of the hydrofoil device are 0.1 W (W is the width of the raceway) and 1.0 Hz, respectively, the anti-Karman vortex streets produced by the hydrofoil device are less affected by the wall, the flow field is the most uniform, the particulate matter discharge performance is the best, and the final floating particulate matter discharge rate reaches up to 99.09%. Adjusting the chord length of the hydrofoil can effectively ameliorate flow field reflux issues, enhancing the uniformity and flow performance of the flow field. When the chord length is 0.1 W, the uniformity of the flow field is optimal. When the chord length is 0.2 W, the flow performance of the flow field is superior. Increasing the frequency enhances the flow performance of the flow field, with an average increase of 0.1 Hz in motion frequency leading to a 19.42% improvement in the average velocity at the outlet. Based on this, we recommend the use of a hydrofoil device with a chord length of 0.1 W and a motion frequency of 1.0 Hz in the raceway aquaculture system to achieve optimal particulate matter discharge performance, providing a theoretical basis and practical guidance for using hydrofoil devices to improve the efficiency of floating particulate matter treatment in raceway aquaculture environments.

A multivariate and wavelet-based analysis on the wall pressure fluctuations for propellers in ground effect

This study, conducted at the University of Bristol’s aeroacoustic facility, explores the aeroacoustic characteristics of a 10-inch APC propeller in pusher configuration within ground effect conditions. Tested at a rotational speed of 7000 r/min, the propeller’s performance was evaluated at varying distances from the ground. Wall pressure fluctuations near the propeller were measured at eight radial points, complemented by far-field acoustic measurements. Consistent with previous research, distinctive thrust and torque behaviours were observed when operating both in and out of ground effect. Notably, a significant noise increase of approximately 5 dB was observed on the ground’s reflected side, while a reduction of about 14 dB was detected on the shielded side. Higher-order statistical analysis such as skewness and kurtosis revealed substantial effects of tip vortex impingement in ground effect conditions. This study applies two-point statistics and the Corcos model to analyze propeller-induced wall pressure fluctuations. The coherence function effectively captures the intricate dynamics of pressure variations across different spatial locations and frequencies. This approach offers novel insights into the behaviour of boundary layers and flow-induced pressures in the context of propellers operating in the ground effect. Wavelet decomposition was utilized to differentiate the influences of the boundary layer and the acoustic field. This comprehensive analysis highlights the intricate dynamics of propeller operation in ground effect, contributing valuable insights to the field of aeroacoustic research.

Flow Mechanism Study on the Effect of Controllable Speed Casing With Different Axial Starting Points on Transonic Compressor Rotor Stability

Abstract The controllable speed casing represents an exploring approach to casing technology, designed to enhance the adaptability of casing in compressors under variable working conditions. This paper developed a numerical study into the effects of the axial starting point of the rotatable ring in the controllable speed casing on stability enhancement and performance. Additionally, the study sought to unveil the action mechanism of the rotating casing on various flow elements within the tip passage. The findings indicated that the optimal axial starting point for achieving the most pronounced stability enhancement effect in each rotating speed of the rotatable ring was located at the tip leading edge. In terms of the flow mechanism, the rotation of the rotatable ring was found to enhance the throughflow of the mainstream and the tip vortex, while exacerbating the backflow of the tip leakage flow, which occurred at middle and rear of the tip clearance and had not evolved into tip vortex.

Comparison of aerodynamic and aeroacoustic characteristics of fixed-pitch and variable-pitch rotors

This research conducts a comparative analysis of the aerodynamic and aeroacoustic characteristics of fixed-pitch and variable-pitch controlled multirotors [i.e., revolution per minute (RPM) and collective pitch control]. The study encompasses single-, twin-, and quad-rotor configurations under hovering flight conditions. The unsteady blade motion is modeled as a function of RPM and pitch, fluctuating with frequency and amplitude. To comprehensively account for wake interaction effects, a free-wake vortex lattice method combined with acoustic analogy is utilized. The findings reveal that unsteady blade motion and wake interaction effects cause fluctuations in thrust and tip vortex trajectory. The thrust and tip vortex behavior exhibited greater instability in response to RPM fluctuations than to pitch fluctuations. Consequently, the axial unsteady loading noise was more pronounced under RPM fluctuations compared to pitch fluctuations. In both twin- and quad-rotor configurations, the wake interaction significantly influenced the characteristics of thrust and tip vortex behavior. In addition, spectral analysis demonstrated that the frequencies of unsteady blade motion and wake interaction determine the frequencies of thrust and tip vortex fluctuations as well as unsteady loading noise.

The best whistler: A cavitating tip vortex

The discrete tone radiated from a cavitating tip vortex, known as “vortex singing,” was first recognized in 1989, but its sound generation mechanism has remained a mystery for over 30 years. In this Letter, by means of the correction for the cavitation bubble dynamics and the dispersion relation of cavity interfacial waves, we found that after the far-end disturbances propagate upstream, the whistling vortex should be triggered by near-end sound sources, the breathing mode waves. Further utilizing the theoretical solutions for singing lines and the potential singing cavitation number with frequency, we accurately identified all available tests for seeking the vortex singing over the past three decades, which not only demonstrates that the vortex singing frequency is only determined by the measurable mean cavity radius (rc), cavitation number (σ), and desinent cavitation number (σd) in experiments, but also responses to a long-standing perplexity: why such a best whistler is able to appear only within a narrow range of the cavitation number.

Lagrangian flow networks for passive dispersal: Tracers versus finite-size particles.

The transport and distribution of organisms such as larvae, seeds, or litter in the ocean as well as particles in industrial flows is often approximated by a transport of tracer particles. We present a theoretical investigation to check the accuracy of this approximation by studying the transport of inertial particles between different islands embedded in an open hydrodynamic flow aiming at the construction of a Lagrangian flow network reflecting the connectivity between the islands. To this end, we formulate a two-dimensional kinematic flow field which allows the placement of an arbitrary number of islands at arbitrary locations in a flow of prescribed direction. To account for the mixing in the flow, we include a von Kármán vortex street in the wake of each island. We demonstrate that the transport probabilities of inertial particles making up the links of the Lagrangian flow network essentially depend on the properties of the particles, i.e., their Stokes number, the properties of the flow, and the geometry of the setup of the islands. We find a strong segregation between aerosols and bubbles. Upon comparing the mobility of inertial particles to that of tracers or neutrally buoyant particles, it becomes apparent that the tracer approximation may not always accurately predict the probability of movement. This can lead to inconsistent forecasts regarding the fate of marine organisms, seeds, litter, or particles in industrial flows.

On the absence of a secondary vortex street in three-dimensional and turbulent cylinder wakes

On the absence of a secondary vortex street in three-dimensional and turbulent cylinder wakes

Exploring multiple phases and first-order phase transitions in Kármán Vortex Street

Kármán Vortex Street, a fascinating phenomenon of fluid dynamics, has intrigued the scientific community for a long time. Many researchers have dedicated their efforts to unraveling the essence of this intriguing flow pattern. Here, we apply the lattice Boltzmann method with curved boundary conditions to simulate flows around a circular cylinder and study the emergence of Kármán Vortex Street using the eigen microstate approach, which can identify phase transition and its order-parameter. At low Reynolds number, there is only one dominant eigen microstate W1 of laminar flow. At Rec1 = 53.6, there is a phase transition with the emergence of an eigen microstate pair W2,3 of pressure and velocity fields. Further at Rec2. = 56, there is another phase transition with the emergence of two eigen microstate pairs W4,5 and W6,7. Using the renormalization group theory of eigen microstate, both phase transitions are determined to be first-order. The two-dimensional energy spectrum of eigen microstate for W1, W2,3 after Rec1, W4–7 after Rec2 exhibit −5/3 power-law behavior of Kolnogorov’s K41 theory. These results reveal the complexity and provide an analysis of the Kármán Vortex Street from the perspective of phase transitions.