Periodic Wake Research Articles

Modelling of wake-induced vibration of a long-span bridge with separated parallel nonidentical decks

The separated parallel decks design for long-span bridges can meet higher traffic demands, offering advantages in urban bridge design. However, when exposed to wind, the periodic wake shedding from the front bridge deck significantly affects the rear deck, leading to wake-induced vibrations (WIV). To address this issue, this study proposes and compares four models to comprehensively predict the wake-induced vibration of a long-span bridge with separated parallel nonidentical decks. The predictive capabilities of the four models for WIV are meticulously compared, and the reasons for the observed errors are analyzed. Ultimately, a model capable of accounting for the concurrent influences of wake-induced forces, instantaneous structural motion feedback, and non-linear self-excited forces is obtained. A series of wind tunnel tests are conducted to validate and evaluate the proposed models. Besides, this study encompasses an analysis of how structural damping and the deck layouts influence WIV. These findings bear substantial relevance to engineering practices confronted with similar challenges, thereby contributing to a deeper understanding of the intricate dynamics at play in such complex structural configurations.

Influence of thermal buoyancy on the wake dynamics of a heated square cylinder

Direct numerical simulation of the three-dimensional (3-D) wake transition of a heated square cylinder subjected to horizontal cross-flow is performed in the presence of buoyancy. In order to capture the effects of large-scale heating, a non-Oberbeck–Boussinesq model is utilized, which includes the governing equations for compressible gas flow. All computations are performed at low free stream Mach number $M=0.1$ using air (free stream Prandtl number, $Pr=0.71$ ) as the working fluid. The 3-D instability modes A and B, which correspond to free stream Reynolds numbers of 180 and 250, are observed with longer and shorter spanwise wavelengths, respectively, and the onset of three-dimensionality is triggered at a Reynolds number of 173. In the presence of buoyancy, baroclinic vorticity production in the near-wake plays an important role for streamwise vorticity generation. The chaotic wake of the Mode-A instability bifurcates into periodic and quasiperiodic wakes at various heating levels, expressed by the overheat ratio, $\varepsilon =(T_w-T_\infty )/T_\infty$ , where $T_w$ and $T_\infty$ are the temperature of the cylinder surface and the ambient air, respectively. At low heating ( $\varepsilon =0.2$ ), the 3-D Mode-A instability is suppressed leading to a two-dimensional wake flow. Further increase in heating, again brings back the three-dimensionality in the wake through Mode-E instability. The variation of thermophysical properties and the effective Reynolds number with increase in heating level around the cylinder is examined. It is shown that the effect of thermophysical properties competes with the baroclinic streamwise vorticity generation at higher levels of heating ( $\varepsilon \geqslant 0.4$ ) to control the 3-D modes and wake dynamics.

Unsteady Interaction Between Purge Flow and Secondary Flow in High-Lift Low Pressure Turbine

Abstract The coupling effect between the complex vortex system and the rim purge flow in the endwall region of a high-lift low pressure turbine (LPT) will significantly influence the evolution of secondary flow and the corresponding losses. This paper focused on the unsteady interaction mechanism between the rim purge flow and the secondary flow inside the high-lift LPT under the periodic wake passing. The large eddy simulation (LES) method was used to reveal the influence mechanism of rim purge flow, rotor-stator cavity interaction and unsteady wakes on the secondary flow. Detailed experimental measurement was carried out for the flow field of high-lift LPT under the influences of static purge flow. The results showed that the rim purge flow significantly increased the overturning and underturning downstream of the endwall region, resulting in aggravating secondary loss. The rotating-rim increased the difference of the circumferential velocity between the mainstream and the purge flow, aggravating the Kelvin-Helmholtz (K-H) instability, inducing the K-H vortex structure with stronger energy amplitude, and further increasing the endwall flow loss. The incoming wakes weakened the energy amplitude of the K-H vortex at the rim purge outlet, thinned the thickness of the low-energy fluid at the blade leading edge. Additionally, the interaction between the wakes and the secondary vortices further suppressed the development of the secondary flow. Nevertheless, the incoming wakes caused additional mixing losses and made a negative impact on the overall aerodynamic performance of the high-lift LPT.

Reduced-order prediction of unsteady spatial-temporal aerodynamics in a turbine cascade

A low-cost prediction method that effectively captures the detailed dynamics of unsteady motions is necessary for turbomachinery design. This paper applies two data-driven methods for unsteady cascade flow of a T106 low-pressure turbine with periodic incoming wakes under unknown conditions and unknown instants, respectively. For the prediction under unknown conditions, the dominant coherent structures of the unsteady flows are obtained using sparsity-promoting dynamic mode decomposition. An arbitrary case's sparse promoting modes serve as a basis for prediction and polynomial interpolation is employed to predict the characteristic parameters, including the amplitude and frequency. Based on the predicted characteristic parameters and sparse promoting modes, the flow fields within a range of Reynolds numbers can be reconstructed. The results show that the large-scale flow structure at different Reynolds numbers can be predicted with reasonable error. The detailed flow structure of cascade flow fields also agrees well with simulation results, demonstrating the method's excellent applicability. For the prediction under unknown instants, the dominant coherent structures of the unsteady flows are obtained using proper order decomposition. The extreme gradient boosting method is utilized to construct a surrogate model and predict the time coefficients at unknown times. Based on the dominating modes and predicted time coefficients, the flow fields within a range of unknown instants can be reconstructed. The cascade flow fields can be recovered with a relative error of less than 3 %. The vortex structures and blade surface pressure agree well with simulation results. The present work provides a promising approach for turbomachinery design and investigating underlying mechanisms with low data requirements.

Optimization of Rotor Tip Cavity Shapes for Mitigating Aerodynamic Tip Leakage Losses

Rotor blade tip leakage loss influences turbine stage efficiency. A parametric optimization method based on five design variables combined with Non-Linear Programming by Quadratic Lagrangian to optimize the turbine efficiency estimated from computational fluid dynamics analysis has been used to obtain estimates of the optimal cavity depth and split rib location within the tip cavity, which appears to improve the stage efficiency by 1.5%. Besides the design point, the influence of the optimized tip cavity shape impacts the performance of the rotor at different rotational speeds and pressure ratios. In this study, by comparing different tip cavity shapes, it is shown that a dual-cavity shape on the rotor blade tip with a stream-direction split rib can effectively control the air flow bending angle inside the tip clearance and improve the aerodynamic performance. The compressible unsteady Reynolds-averaged Navier–Stokes model is used to verify the adaptability of the optimized tip cavity shape to periodic wake disturbances, and the results demonstrate that the time-averaged estimate of the efficiency can be improved by 1.3% compared to that of the flat rotor tip.

Optimal waveform for fast synchronization of airfoil wakes

We obtain an optimal actuation waveform for fast synchronization of periodic airfoil wakes through the phase reduction approach. Using the phase reduction approach for periodic wake flows, the spatial sensitivity fields with respect to the phase of the vortex shedding are obtained. The phase sensitivity fields can uncover the synchronization properties in the presence of periodic actuation. This study seeks a periodic actuation waveform using phase-based analysis to minimize the time for synchronization to modify the wake shedding frequency of NACA0012 airfoil wakes. This fast synchronization waveform is obtained theoretically from the phase sensitivity function by casting an optimization problem. The obtained optimal actuation waveform becomes increasingly non-sinusoidal for higher angles of attack. Actuation based on the obtained waveform achieves rapid synchronization within as low as two vortex shedding cycles irrespective of the forcing frequency, whereas traditional sinusoidal actuation requires ${O}(10)$ shedding cycles. Further, we analyse the influence of actuation frequency on the vortex shedding and the aerodynamic coefficients using force-element analysis. The present analysis provides an efficient way to modify the vortex lock-on properties in a transient manner with applications to fluid–structure interactions and unsteady flow control.

Direct Numerical Simulation of a High-Pressure Turbine Stage: Unsteady Boundary Layer Transition and the Resulting Flow Structures

Abstract In the present study, we investigate the unsteady boundary layer transition based on the direct numerical simulation database of a high-pressure turbine (HPT) stage (Zhao and Sandberg, 2021, High-Fidelity Simulations of a High-Pressure Turbine Stage: Effects of Reynolds Number and Inlet Turbulence, ASME Turbo Expo 2021, Paper No. GT2021-58995), focusing on the transition mechanisms on the rotor blade, affected by the incoming periodic wakes and the background freestream turbulence (FST). On the basis of the fully resolved flow fields, we provide detailed analysis of the flow structures responsible for the transition, and two distinctive transition paths have been identified. The first path is the typical bypass transition via the instability of Klebanoff streaks, which happens when the transition region is not directly affected by the wake. The suction-side boundary layer is disturbed at the leading edge, resulting in the formation of streamwise streaks. These streaky structures endure varicose instability in the region with adverse pressure gradient (APG), then quickly break down into turbulent spots, which then evolve into fully turbulent flow. The other transition path is a consequence of the direct interaction between the wake structures and the blade boundary layer, when the wake apex starts to affect the transitional region. To be specific, the wake structures directly interact with the separation bubble in the APG region, causing sudden breakdown into turbulence. A calmed region is found to follow the wake-induced turbulent boundary layer. It is observed that the recovery to a calmed region can be impacted by the FST, as the calmed region in case with no FST is much longer compared to cases with stronger FST.

Effects of Periodic Incoming Wakes on the Aerodynamics of a High-Speed Low-Pressure Turbine Cascade

The influence of unsteady wakes incoming from the upstream stages is of high relevance in modern high-speed, low-pressure turbines (LPT) operating at transonic exit Mach numbers and low Reynolds numbers for their potential to trigger transition and influence the separation of the boundary layer on the blade suction side. The aim of this paper is the experimental characterization of the influence of incoming wakes on the 2D aerodynamics of a high-speed LPT cascade operating at a low Reynolds number and transonic exit Mach number. A detailed analysis of the status of the flow along the blade under investigation and its impact on the profile loss are presented for a range of Mach numbers from 0.70 to 0.95 and Reynolds numbers from 70k to 120k under steady and unsteady inflow conditions. Tests were conducted at on- and off-design engine realistic conditions in the VKI S-1/C wind tunnel on the SPLEEN C1 transonic cascade. The wakes incoming from an upstream blade row have been replicated using a set of rotating bars, which shed wakes at an engine-representative reduced frequency (f+=0.95) and flow coefficient (Φ=0.80). A set of densely instrumented traversable blades were used to sample the surface pressure distributions. The development of the boundary layers along the blade suction side is examined through quasi-wall shear stress obtained with surface-mounted hot-film sensors. Wake traverses were carried out downstream of the cascade with a miniaturized L-shaped five-hole probe to characterize the blade losses. The introduction of periodic incoming wakes promotes variations in the flow topology over the blade. The effect on the suction side separation bubble is shown to depend on the exit flow conditions. At low Mach numbers, the incoming wakes determine a reduction in the size of the bubble; in contrast, this effect is not registered as the exit Mach number increases. Consistently, a high dependence of the unsteady wake effect on the profile loss on the exit Reynolds and Mach numbers is demonstrated.

Analysis of Interaction between Leakage Flow and Upstream Wake by Proper Orthogonal Decomposition Applied

The turbine blade generally works in severe aerodynamic environments such as high temperature and high pressure. Various forms of secondary flow, unsteady potential flow, periodic wake in the blade passage, and strong interactions among these flow structures affect the efficiency of the turbine seriously. This paper performs a numerical simulation of the T106 cascade to investigate the flow characteristics and performance under the interaction between upstream wake and leakage flow. The cascade flow with and without upstream wake are decomposed by proper orthogonal decomposition, and the mode characteristics of leakage flow and wake are obtained. The results indicate that periodic wake can significantly reduce the energy loss in the channel and tip leakage flow has a greater impact in the region near the shroud plane. According to the proper orthogonal decomposition, the second to seventh modes account for 96.14% of the total energy except for the time-averaged mode. The second mode is identified as the wake mode and leakage flow can significantly increase vorticity in the tip region. The harmonics of the wake mode are greatly affected by leakage flow, especially at the trailing edge region.

Compressibility effects on the secondary instabilities of the circular cylinder wake

With a growing interest in low Reynolds number compressible flows, compressibility effects on the secondary instabilities developing on the circular cylinder periodic wake are investigated. The unsteady and time-averaged two-dimensional flows are characterised for Reynolds numbers ${{Re}} \in [200;350]$ and Mach numbers up to ${{M}}_{\infty }=0.5$ , revealing different flow structures which influence the characteristics of the secondary unstable modes. The two-dimensional time-periodic solution is used as the base state for a global linear stability analysis performed by means of Floquet theory coupled with a time-stepping finite-difference approach of the nonlinear operator. The influence of compressibility on mode A and mode B secondary instabilities which are responsible for the three-dimensionalisation of the two-dimensional periodic wake is analysed. A stabilising or a destabilising effect of compressibility is observed on mode A, depending on the Reynolds number and the spanwise wavelength of the mode, while mode B is stabilised by the increase of the Mach number. Compressibility is indeed found to decrease the mode kinetic energy production due to base flow shear conversion, which drives the growth of mode B. This results in a delay of the three-dimensionalisation process of the wake due to compressibility.

Visual analysis of the impact of periodic wakes on the pressure side of a turbine blade

Turbines are core components in jet engines for flight propulsion, power plants, and other important energy conversion processes. They are composed of successive rows of blades so that wakes of upstream blades reach subsequent blades where they perturb the flow in an unsteady manner. At the point where a wake reaches the downstream blades, the perturbation forms a so-called negative jet. In this work, we show that the negative jet partially fulfills the conditions of an anti-splat. Based on this finding, we enhance an anti-splat detection algorithm developed by the present authors in previous work and apply it to direct numerical simulation data of a turbine cascade with unsteady wakes. This provides a sound framework and suitable visualization approaches to investigate the phenomenon even in very complex conditions, as is the alteration of the boundary layer flow along the pressure side of a turbine blade. The approach allows a very clear visualization of this interaction, which was not possible to evidence with previous methods, providing new insight into the physics of this flow. The use of flow paths shows up to which point wakes affect the boundary layer along the blade. The reported physical analysis, made possible by the proposed approach, demonstrates the usefulness of the method for the application domain. The generalization to flows in compressors, pumps, and blade-tower interaction in wind engineering and other fields is possible.Graphical abstract

Aerodynamic performance of high-lift blades in low-pressure turbines with periodic upstream wakes

Aerodynamic performance of high-lift blades in low-pressure turbines with periodic upstream wakes

Vortex dynamics and associated turbulence production in the separated transitional flow and the wake at a moderate Reynolds number

The vortex dynamics in the separated transitional flow and the near-wake over a C4 compressor blade at Rec = 24,000 and incidence angles of 0°, 2.5°, 5°, 7.5°, and 10° are investigated experimentally. The laminar separation vortex shedding, the trailing edge vortex shedding, and the interaction of the two vortices are captured using the time-resolved particle image velocimetry. To separate the contributions to the overall turbulence production due to various flow dynamics, the orthonormality of proper orthogonal decomposition modes of the velocity components is utilized. When the laminar separation is close to the trailing edge, the laminar separation vortex locks in the wake instability with an approximately subharmonic of the von Karman frequency. Approximately 80 % of the turbulence is produced by the large-scale flow structure governed by the laminar separation vortex and trailing edge vortex. When the shear layer separates near the leading edge, the laminar separation vortex shedding frequency is lower with a smaller streamwise wavelength. The turbulence production rate contributed by the laminar separation vortex shedding increases with incidences. These novel experimental findings offer insight into transition mechanisms and turbulence modeling of the separated flow located near periodic wake flow.

Large eddy simulations of periodic wake effects on boundary-layer transition of low-pressure turbine cascades

The periodic wake effect is one of the most important sources of unsteady disturbance in turbines. Its influence on the boundary layer transition process of the downstream blade suction surface is an important factor determining the turbine loss and aerodynamic performance, and also an effective potential approach of turbine loss control. In this paper, the high-load low-pressure turbine (LPT) cascade is taken as the research object, and the large eddy simulation based on the inhouse coed Multiblock Parallel Large-eddy Simulation is used to study the periodic influence of upstream wake. The unsteady transition process of the boundary layer on the suction surface of the turbine cascade and the spatial–temporal evolution of the vortex are discussed in detail. It is shown that there are three modes of boundary layer transition on the suction surface of the LPT cascade under the effect of wake, occurring alternately during the wake passing period. Each mode of transition has different characteristics in vortex structures, as well as boundary-layer separation and reattachment, thereby makes different losses. Although the transition mechanism and evolution process of the three modes are different, the calming regions exist in all three modes, which is important for the control of the boundary layer. This study gives an important reference for reducing the flow loss in high-load turbines by means of periodic wakes.

Image and video compression of fluid flow data

We study the compression of spatial and temporal features in fluid flow data using multimedia compression techniques. The efficacy of spatial compression techniques, including JPEG and JPEG2000 (JP2), and spatiotemporal video compression techniques, namely H.264, H.265, and AV1, in limiting the introduction of compression artifacts and preserving underlying flow physics are considered for laminar periodic wake around a cylinder, two-dimensional turbulence, and turbulent channel flow. These compression techniques significantly compress flow data while maintaining dominant flow features with negligible error. AV1 and H.265 compressions present the best performance across a variety of canonical flow regimes and outperform traditional techniques such as proper orthogonal decomposition in some cases. These image and video compression algorithms are flexible, scalable, and generalizable holding potential for a wide range of applications in fluid dynamics in the context of data storage and transfer.Graphic abstract

Two- and three-dimensional wake transitions of a NACA0012 airfoil

Flow transitions are an important fluid-dynamic phenomena for many reasons, including the direct effect on the aerodynamic forces acting on the body. In the present study, two-dimensional (2-D) and three-dimensional (3-D) wake transitions of a NACA0012 airfoil are studied for angles of attack in the range $0^\circ \leq \alpha \leq 20^\circ$ and Reynolds numbers $500 \leq {\textit {Re}} \leq 5000$ . The study uses water-channel experiments and 2-D and 3-D numerical simulations based on the nodal spectral-element method, level-set function-based immersed-interface method and Floquet stability analysis. The different wake states are categorised based on the time-instantaneous wake structure, non-dimensional frequency and aerodynamic force coefficients. The wake states and transition boundaries are summarised in a wake regime map. The critical angle of attack and Reynolds number for the supercritical Hopf bifurcation (i.e. steady to periodic wake transition) varies as $\alpha _1 {\sim} {\textit {Re}}^{-0.65}$ , while the critical angle of attack for the onset of three dimensionality varies as $\alpha _{3D} {\sim} {\textit {Re}}^{-0.5}$ . Over the entire Reynolds number range, the transition to 3-D flow occurs through a mode C (subharmonic) transition. Beyond this initial transition, further instabilities of the 2-D periodic base flow arise and are investigated. For instance, at $ {\textit {Re}}=2000$ and $\alpha _{3D,2}=11.0^\circ$ , mode C coexists together with modes related to modes A and QP seen in a stationary circular cylinder wake. In contrast, at $ {\textit {Re}}=5000$ and $\alpha _{3D,2}=8.0^\circ$ , the dominant mode C coexists with mode QP. Three-dimensional simulations well beyond critical angles indicate that 2-D vortex-street transitions are approximately maintained in the fully saturated 3-D wakes in a spanwise-averaged sense.

Effect of arc‐shaped vertical control plate on heat and mass transfer in uniform flow past an isothermally heated circular cylinder

AbstractThe current work investigates the effect of an arc‐shaped vertical control plate on the heat and mass transfer in uniform flow past an isothermally heated circular cylinder. The control plate is positioned downstream at various distances from the circular cylinder's surface. The governing equations are discretized by the higher order compact (HOC) finite difference scheme, and then this system of discretized equations is solved by using a bi‐conjugate gradient stabilized iterative method for Prandtl number , Reynolds number . To investigate the effect of an arc‐shaped control plate on heat and mass transfer, we consider a range of nondimensional distances between the circular cylinder and the control plate, , where is the control plate's distance and is the cylinder's radius. The exact timing and location of the bifurcation points are calculated by using topological aspect‐based structural bifurcation analysis. Significant effects of various locations of the control plate on periodic wake and heat transfer are observed. It is found that the increasing distance of the control plate from the cylinder delays the occurrence of the structural bifurcation and shifts the bifurcation points upwards in the upper half and downwards in the lower half of the cylinder. Our study shows that the specific location of the control plate can fully suppress the vortex shedding. Time‐averaged total Nusselt number can be drastically reduced by increasing the distance between the control plate and the cylinder. With proper positioning, the vertical control plate can lessen the time‐averaged drag force by up to when compared to a cylinder without a control plate. Overall, this work presents many new phenomena that have not been reported before.

Post-stall flow control with upstream flags

The post-stall flow control using compliant flags of varying thickness and length, placed upstream a NACA0012 airfoil, was shown to be possible at an airfoil chord Reynolds number of 100,000. The flag wakes produced substantial increase in the stall angle and the maximum lift coefficient of the airfoil placed at optimal cross-stream locations from the wake centerline. Oscillating flags could generate periodic wakes with better spanwise coherence than the stationary bluff body. This resulted in the excitation, formation and shedding of the leading-edge vortices periodically, providing mean lift enhancement. There is an optimal range of the flag mass ratio for which the flag frequency coincides with the natural frequency of the vortex shedding instability or its subharmonic of the baseline airfoil wake. The flag dimensionless frequency is a function of the mass ratio only, which can be predicted by a reduced order model in the limit of very large mass ratio and by using the modified free-streamline theory for the separated flow. There is also an optimal range of the flag dimensionless frequency.Graphical abstract

Profile Loss Reduction of High-Lift Turbine Blades With Rough and Ribbed Surfaces

Abstract Transitional boundary layers on low-pressure turbines (LPTs) are prone to separation on the suction surface of the blade under strong local adverse pressure gradients. Intermittent freestream turbulence, periodic wakes shed by the upstream blades, and surface roughness due to in-service degradation of the blades are shown to suppress the separation. Although this generally leads to a profile loss reduction, some of the benefits are offset by a loss increase associated with an increased turbulent wetted area. In this work, we explore a strategy where the losses in both the transitional and turbulent boundary layers can be reduced. In particular, we employ surface roughness in the transitional regime to reduce the separation bubble-related losses and riblets in the turbulent regime to further reduce the losses due to the turbulent wetted area. The efficacy of this ‘rough-riblet blade surface’ is studied using high-fidelity eddy resolving simulations on the configuration of a flat surface subjected to streamwise varying pressure gradients. Two riblet shapes, sawtooth and scalloped, are considered. When compared to the roughness alone configuration, scalloped riblets reduced the skin friction drag by ≈10% and are much more effective than the sawtooth riblets. Through the streamwise evolution of the boundary layer parameters such as trailing edge momentum thickness, maximum turbulent kinetic energy, and Reynolds stresses, the additional losses incurred at the junction between the smooth wall and riblet leading edge are highlighted.

Unsteady Effects of Wake on Downstream Rotor at Low Reynolds Numbers

In a compressor, the periodic wake is an inherently unsteady phenomenon that affects the downstream flow conditions and loading distribution. Thus, understanding the physical mechanisms of these unsteady effects is important for eliminating flow losses and improving compressor performance, particularly at low Reynolds numbers. To understand the influence of the upstream wake on the downstream flow field structure, this paper describes numerical simulations of a one-stage high-pressure compressor at altitudes of 10–20 km. The influence of the wake on rotor flow blockage at different Reynolds numbers is analyzed, and the unsteady interaction between the upstream wake and boundary layer or tip leakage flow is discussed. The results indicate that the wake has a beneficial effect on the efficiency of the rotor at high Reynolds numbers, but this weakens and becomes negative as the Reynolds number decreases. The wake can reduce the flow blockage in the mainflow region. Due to the wake, the length of the laminar separation bubble at high Reynolds numbers decreases and that at low Reynolds numbers increases. In addition, the unsteadiness of the wake causes separation bubbles to appear periodically at high Reynolds numbers and induces an open separation bubble at low Reynolds numbers. The Kelvin–Helmholtz instability can dominate the transition process of the boundary layer, which is also affected by the disturbance vortex induced by the wake. Regarding the tip leakage flow, the wake can reduce the flow blockage at high Reynolds numbers but increase the flow blockage at low Reynolds numbers. The interaction at low Reynolds numbers causes a double-leakage flow, which finally leads to the large-scale separation of the suction surface boundary layer. The large-scale separation causes flow blockage in the tip region and prevents the rotor wake from propagating downstream. On the contrary, the unsteady wake can pass through the tip clearance vortex and inhibit the separation of the suction boundary layer at high Reynolds numbers, which is reflected in a larger amplitude of one blade passage frequency. Therefore, the flow loss in the downstream flow field at high Reynolds numbers is significantly reduced at high Reynolds numbers.