Proper Orthogonal Decomposition Analysis Research Articles

Effect of Gas Addition on Liquid Kerosene Combustion in a Scramjet Combustor

Experiments were conducted at Mach 2.52 to investigate the effect of gas addition on the mixing and combustion characteristics of the liquid kerosene in a scramjet combustor. Two different combustion modes (scram mode and ram mode) were achieved by varying the equivalence ratio. Flowfield diagnostic techniques, such as shadow visualization and wall pressure measurement, and Proper Orthogonal Decomposition analysis were employed to investigate the complex supersonic gas– liquid two-phase combustion flowfield. It is found that, compared to the pure high-pressure kerosene, the gas-added kerosene can achieve better combustion performance at low injection pressure. The gas addition increases the fuel-jet penetration depth and promotes flowfield fluctuations. The gas–liquid two-phase instability induces large-scale vortices within the fuel-jet shear layer. The diffusion and mixing of kerosene are enhanced by the large-scale vortices, and the rapid and intense combustion of kerosene is realized.

Flapping dynamics of a flexible membrane attached to the leading edge of a forward-facing step

The flapping dynamics of a flexible membrane (FM) and its effect on the flow fields over and pressure fluctuations on a forward-facing step (FFS) have been investigated experimentally. The two-dimensional FM with 40 mm in length and 0.15 mm in thickness was vertically attached to the leading edge of a FFS with 40 mm in height. The deformation of the flapping FM was recorded by a high-speed camera. Velocity data in the vertical central plane and the pressure fluctuations on the step surface were measured by planar particle image velocimetry and pressure sensors, respectively. The results demonstrate that as the dimensionless bending rigidity (γ) of the FM decreases, the FM displayed two distinct modes, i.e., the bending mode and the flapping mode. In the bending mode, the bent FM is similar to a curved barrier, which elevates the shear layer and delays the reattachment of separation flow. In the flapping mode, the amplitude of the FM increases with the decrease in γ, which in turn effects the scale of flapping-induced vortices (FIVs). In proper orthogonal decomposition analysis, the results reveal a transition in the dominant flow structure from large-scale separation to FIVs with reducing γ. The FIVs significantly affect the pressure distribution on the step surface of the FFS, and the range where the coherent contribution dominates expands with the decreasing γ.

Enhancement of aerodynamic performance of Savonius wind turbine with airfoil-shaped blade for the urban application

The present study introduces a novel rotor configuration with an airfoil-shaped blade, based on the low-speed high-lift FX74-CL5-140 airfoil, for enhancing the performance of the Savonius wind turbine for a practical application in urban areas. The preferment of the present design over the original one with a semicircular shape is confirmed by the sequence of unsteady two-dimensional (2D) numerical simulation. The results demonstrate a new power coefficient peak (up to 16.5 % better than that of the original rotor) could be gained at the tip speed ratio (TSR) of 1.1. The effective working range is further extended to TSR > 0.7 compared to that at TSR > 1.0 in the literature. Insight into the flow dynamic, including pressure, velocity, streamline, and wake analysis, reveals that the thick blade near the overlap region, benefiting in terms of the turbine’s high performance. The airfoil blade increases the momentum energy around the rotor, changes the pressure on the concave side, and varies the origin of the pressure force, leading to an increase in the moment arm with more torque exhibited on the rotor at high TSR. In addition, the proper orthogonal decomposition (POD) analysis is also performed to better understand the flow phenomena behind the rotor. Overall, the present design is beneficial for urban applications because it can enhance the rotor performance without losing the omnidirectional and compactness features.

Insights into turbulent flow structure and energy dissipation in centrifugal pumps: A study utilizing time-resolved particle image velocimetry and proper orthogonal decomposition

The purpose of the study is to investigate the flow structure and energy dissipation mechanism within centrifugal pump impellers. The velocity fields at the mid-sections of the flow passages of 4- and 5-blade impellers were measured under various flow rates using the Time-resolved Particle Image Velocimetry (TR-PIV) technique; the proper orthogonal decomposition (POD) analysis was performed to extract flow structures with different scales; the dissipation rate was estimated using the large-eddy PIV method; the correlation between turbulent kinetic energy (TKE) and dissipation rate was measured using the cross-correlation analysis. The findings are as follows: impeller with more uniform and stable flow, the scale and energy contribution of large-scale structures in lower order modes are smaller, leading to higher impeller efficiency; large-scale structures identified in the low-order modes correspond to locations of high TKE and dissipation areas; the high velocity gradients within the impeller passage and the interactions between large-scale flow structures encourage the breakup of large-scale turbulent structures into dissipative-scale structures; the correlation between TKE and dissipation rate reflects the extent to which large-scale flow structures within the impeller passage break up into dissipative scales.

Investigation of Unsteady Combustion Regimes in a Kerosene-Fueled Scramjet with Air Throttling

This paper describes an experimental study investigating unsteady combustion regimes in a kerosene-fueled scramjet. The results are obtained under inflow conditions of a 2.9 MPa stagnation pressure, 1900 K stagnation temperature, and a Mach number of 3.0. The air throttling position is 240 mm downstream of the combustor entrance, with an air throttling flow rate (ratio of air throttling mass flux to inflow mass flux) of 38% and a fuel equivalence ratio of 0.37. Combustion is relatively stable when air throttling is applied and is dominated by auto-ignition. When air throttling is turned off, the combustion becomes more unsteady and is dominated by flame propagation. At the same time, the combustion mode changes, and the frequency of the combustion mode transition is 286 Hz. Schlieren images and one-dimension analysis show that the effect of air throttling is the coupling of cold throat (aerodynamic throat) and hot throat (thermal throat). The proper orthogonal decomposition and dynamic mode decomposition analysis present that when air throttling is applied or removed, the frequencies of injector–flame feedback are almost the same, while the frequencies of shock–flame feedback exhibit considerable variation, which is caused by the location of the precombustion shock affected by air throttling.

Investigation of pulsed direct-current plasma jets in a turbulent boundary layer

Characteristics of the plasma jet produced by a pulsed direct-current (pulsed-DC) dielectric barrier discharge (DBD) and its interaction with a turbulent boundary layer (TBL) are investigated in detail using stereo particle imaging velocimetry. Quiescent-flow characterization results show that a positive starting vortex and a negative near-wall jet structure are induced by the pulsed-DC DBD plasma actuator. With increasing pulse width and discharge frequency, the jet velocity magnitude increases monotonously, as a direct result of the extension of fluid particle acceleration time. During the interaction with a cross-flow TBL, two streamwise vortices with opposite signs are observed at the two sides of the electrode junction, which essentially originate from the starting vortex and negative jet in quiescent air. The skin-friction drag variations are dominated by the cross-stream momentum transportation of streamwise vortices, with drag reduction in the vortex upwash zone and drag increase in the downwash zone. Compared with the conventional alternating-current DBD plasma actuators, the turbulent fluctuations produced by pulsed-DC DBD are much higher, which also affects the skin-friction drag. Further proper orthogonal decomposition (POD) analysis reveals that two distinctly different flow patterns are produced by pulsed-DC DBD working at small and large pulse widths. The dominant POD modes causing the most velocity fluctuation are the spanwise translation and deformation of plasma-induced streamwise vortices. These results provide insights into the basic phenomenon of pulsed-DC plasma jets in cross flow, which recently has demonstrated its promising applications in turbulent skin-friction reduction.

Data-driven modal decomposition of R134a refrigerant cavitating flow in Venturi tube

This study utilized high-speed camera and large eddy simulation methods to explore the cavitating flow mechanisms and turbulence structures of R134a refrigerant inside a Venturi tube under varying cavitation numbers (CNs). Data-driven modal analysis approaches, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), were introduced to identify and extract the energy hierarchy and transient characteristics within the cavitating flow. The analysis of grayscale images indicated that the cavitating flow gradually transitioned from quasi-periodic to unsteady flow as the CN decreased, and the severity of cavitation correlates with lower peak frequencies. The POD analysis facilitated the extraction of coherent structures in the cavity's temporal evolution, and the results indicate that the quasi-ordering shedding and collapse of large-scale cavity clouds predominantly occur under low cavitation intensity conditions. As the CN increases, the influence of small-scale cavity shedding becomes more significant. The first 30 most energetic modes occupied over 75% of the entire energy, and they were used to reconstruct the cavitating flow, achieving good consistency with transient flow snapshots. Additionally, the DMD results of the cavitating flow yield three frequency spans, including several prominent characteristic frequencies. These spans are closely linked to the cavity cloud structures of varying scales, unveiling the structural characteristics of unsteady cavitating flow.

Experimental study of turbulent flow in lower plenum with flow skirt of reactor pressure vessel of pressurized water reactor

The turbulent flow in lower plenum of reactor pressure vessel (RPV) of pressurized water reactor (PWR) is an important phenomenon for design of flow mixing device. A high-precision matched index of refraction (MIR) technique is requisite for time-resolved particle image velocimetry (TR-PIV) measurements in RPV with complicated internals. In this study, turbulent flow in a scaled-down RPV model was measured by TR-PIV under different Reynolds numbers (Re) and asymmetrical flow rate with aid of the high-precision MIR technique of sodium iodide (NaI) solution and acrylic. The time-averaged flow structures include flow separation at the corner of lower support plate, fluid bifurcation around the lower edge of flow skirt, flow turning upward below the vortex suppression plate, horizontal jets at holes of flow skirt, vertical jets at holes of vortex suppression plate, improving turbulent mixing and Reynolds stresses in the lower plenum. The coherent structures were studied by proper orthogonal decomposition (POD) analysis. The flow skirt and vortex suppression plate break down large vortices through them. With Re increasing, Reynolds stresses decrease fast, and the energy fractions of low-order modes transfer into high-order modes, because turbulent vortices break up. In the case of asymmetrical flow rate, the time-averaged velocity and Reynolds stress decrease slightly, and the cumulative energy fraction decreases at flow skirt and vortex suppression plate.

Experimental investigation on the effects of transverse injection distribution scheme on dual flame dynamics subjected to flow disturbances

Combustion instability has become a major problem in low-emission annular gas turbine combustors. It is of practical importance to investigate the effects of transverse nozzle distribution scheme on multi-flame dynamics subjected to external acoustic perturbations. In this study, the responses of heat release rate perturbations from dual propane/air laminar premixed flames to axial acoustic perturbations have been experimentally measured. Specifically, the velocity disturbance upstream the flame base has been measured by two-microphone method and the flame heat release rate perturbation is obtained by the photomultiplier tube with CH* filter lens. The dynamic evolution of dual flames is captured by the high-speed camera and then analyzed with the proper orthogonal decomposition (POD) method. Results indicate that there is a critical distribution distance, where the peak gain of the dual flame transfer function is the largest. And the direct injection dual flame transfer function can behave as the low-pass filter. Furthermore, the dual flame transfer function behaves nonlinearly with the increase of the injection angle. The dual flame transfer function for large injection angle can behave as the hybrid mode of the low-pass filter and the band-pass filter. The POD analysis reveals that the coupling effect of gas thermal expansion and stretch effect would contribute to the interaction between dual flame front dynamics. The transverse injection distribution scheme (dual flame distance and injection angle) has a significant effect on the dual flame front dynamics, which in turn affects the flame heat release rate disturbance. The bulk mean flow velocity can enhance the interaction effect between dual flame front dynamics.

Influence of gap thickness on aerodynamic forces and flow structures of circular cylinders under passive-suction-jet control

A parametric study of the passive-suction-jet control scheme was experimentally performed for the cylinder model. The dependence of the control effectiveness on the gap thickness was determined for a cylinder model controlled by passive-suction-jet pipes at Reynolds number (Re) values ranging from 20,000 to 60,000. The fluid forces and flow structure were measured on a cylinder model without any control and used to evaluate the control effectiveness. Proper orthogonal decomposition (POD) analysis, phase average, and triple decomposition were applied to the flow fields to explore the control mechanism. The results show that the pipe control was most effective when the gap thickness was 0.075D. Too large or too small a gap thickness was not beneficial for controlling the resistance level, and the fluctuating lift was reduced to a tiny level as the thickness increased to 0.075D. The steady jets ejected from the leeward slots rolled up into several small-scale standing vortices. These vortices modified the streamline topology of the model, developing a new saddle point in the wake. Moreover, the roll-up of the separated shear layers was restrained by the pipe, which inhibited the vortex formation and shedding processes and the unsteady forces exerted on the model.

PIV measurements of coherent vortices and turbulence production inside acoustic liner cavity with offset slit

This paper reports an experimental investigation into the vortex dynamics purely excited by periodic acoustic waves within a slit–cavity structure, which is a typical unit element of an acoustic liner for aeroengine applications. Particle image velocimetry (PIV) was used to measure the instantaneous, time-averaged and phase-dependent flow dynamics inside the slit–cavity, which is exposed to high-intensity incident acoustic waves. Different with traditional literature mainly focusing on the acoustic characteristics, we primarily analyze the coherent vortex structures and turbulence production mechanism, accompanying with the variable of slit offset ratio being taken into consideration. The results demonstrate that the acoustic waves can excite the hydrodynamic velocities exceeding almost tens of times than the acoustic particle velocity, yielding multi-scale vortex structures appearing within the enclosed volume. Comparatively, in configuration with offset slit, the maximum hydrodynamic velocities were gradually intensified by wall confinement effect. Subsequent proper orthogonal decomposition analysis revealed the coherent vortex structures and demonstrated the offset configuration will increase their energy proportions and enhance their temporal correlations. However, the phase-dependent flow results revealed that the offset slit can oppositely attenuate the kinematics of the coherent vortices, which were represented by the convection trajectories and convection speeds, especially during the initial acceleration stage. Finally, analysis on turbulence production mechanism confirmed the attenuated turbulent kinetic energy by the offset slit, which was attributed to the less generation of shear stresses.

Nonlinear supersonic flutter of a composite panel backed by an acoustic cavity with finite-amplitude sound waves

In this paper, an implicit partitioned fluid-structure-acoustic interaction method is presented for predicting nonlinear aeroelastic response of an elastic composite laminated panel backed by an acoustic cavity and subject to a supersonic flow. The method is formulated in an arbitrary Lagrangian-Eulerian framework based on the unsteady Navier-Stokes equations for the supersonic flow, a geometrical nonlinear dynamics model for the composite laminated panel, and the nonlinear Westervelt equation for the finite-amplitude sound waves in cavity. A theoretical fluid-structure-acoustic model of the supersonic panel is proposed for validating the present numerical method, in which the nonlinear structural model of the panel, the first-order piston aerodynamics model of the supersonic flow and the nonlinear sound wave model of the cavity are coupled in a monolithic manner. It is found that cavity acoustic resonance can appear in the case a vibration mode of the panel coalescing with an acoustic mode of the cavity. Several new physical features of nonlinear acoustic resonance have been discovered, such as the presence of shock wave with high pressure gradients travelling along the resonant cavity in axial direction and the presence of higher-order harmonic wave components, which emphasize a nonlinear acoustic wave model of the cavity must be used to fully characterize these phenomena. In addition, the nonlinearity of the standing wave is quantitatively related to the acoustic modes by means of a proper orthogonal decomposition analysis.

Experimental study of flag fluid–structure interaction in a laminar jet and application of POD

A fluttering flag in a uniform laminar flow exhibits complex fluid–structure interaction (FSI) behavior. This investigation experimentally studied aerodynamic load behavior and its connection to the oscillation behavior, flag envelope and fluid flow parameters, and application of Proper Orthogonal Decomposition (POD) to fluid flow data to elucidate changes in flow behavior associated with the changes in oscillation modes and observed drag coefficient values. For this purpose, three flag models with varying lengths were used. The aerodynamic load forces were measured using a high-precision load cell, and two-dimensional Particle Image Velocimetry (PIV) was used to quantify the flow field around the flag. The Reynolds number (Re), mass ratio (R1), and dimensionless rigidity (R2) values were varied between 4.4×104−12.3×104, 1.48−2.77, and 1.3×10−3−15.1×10−3, respectively. The results showed the linear relationship between drag coefficients with normalized amplitude of oscillation and Strouhal number. The results also showed the connection between observed drag and change in flag oscillation modes. The POD analysis showed that the energy content of the POD modes changed with the change in flag oscillation from mode-2 to mode-3 oscillations. The phase portrait of the first four POD modes also showed a unique interplay of POD modes, resulting in a change in the velocity flow field associated with the change in oscillation modes. The low-order reconstruction using select POD modes and control volume analysis of the velocity flow field showed a connection between POD modes and observed drag.

An experimental investigation of the flow control of a circular cylinder in near wake with parallel plates at Re = 7500

The vortex street suppression in the near wake region of the cylinder with parallel plates was investigated using particle image velocimetry (PIV) at Reynolds number of Re = 7500. The rigid plates are designed as flat, parallel with the free-stream direction, and located on both sides of the cylinder. Two different plate lengths (0.5D and 1D based on the cylinder diameter, D) were examined at gap ratios of g/D = 0.1, 0.3, 0.5, 0.7, and 0.9, respectively. Proper Orthogonal Decomposition (POD) analyses were also employed to reveal vortex mechanism in the near wake region. The gap ratio significantly influences the interaction of the vortices. At low gap ratios, the plates directly affect the development of shear layers on both side of the cylinder. The shear layers elongate downstream with a reduction of the vortex shedding frequency. Moreover, Reynolds shear stress, vortex shedding instabilities and vortex street are suppressed in the near wake region with the help of using parallel plates. On the other hand, vortex shedding reinforces instabilities at higher gap ratios. Besides, the most effective gap ratio is different for each the plate lengths to suppress instabilities.

VIV of two rigidly coupled side-by-side cylinders at subcritical [formula omitted

Cross-flow vortex-induced vibration (VIV) of two rigidly coupled circular cylinders in side-by-side arrangement at a Reynolds number of 1000 is numerically investigated using direct numerical simulation. A low mass ratio of 1.27 is considered and the nondimensional centre-to-centre spacing ratio is fixed at 2.0. The reduced velocity ranges from 2 to 13. Three response branches are identified and these responses result in different wake and hydrodynamic characteristics. The cases with large amplitudes feature the co-shedding and lower pressure in the gap, while those with small amplitudes are characterised by two parallel vortex streets. Characterisation and quantification of the flow fields of two rigidly coupled side-by-side cylinders undergoing VIV, which have seldom been reported in the existing research, are elaborated on in this study via the statistical analysis in terms of the turbulent wake visualisation, Reynolds stresses, turbulence kinetic energy (TKE) and proper orthogonal decomposition (POD) analysis. It is found that the cases with large amplitudes show a more unstable wake with sharp increases in the Reynolds stresses and TKE in the near wake. Moreover, the large amplitudes are seen to weaken the asymmetry of the wake and the initial POD modes are more energetic. A reformulated version of the novel force decomposition technique is used to realise the measurement of the time-dependent contributions from each mode to the pressure drag. The large amplitude cases are associated with the drag mode and the lift mode, whereas three modes are observed as the amplitude decreases.

Laser interferometric detection of heat release rate perturbation field of acoustically perturbed laminar premixed flames

Laser interferometry, which was originally used to measure density perturbation, has been previously used to determine the heat release rate perturbation, which is a key factor in the analysis of combustion instability. However, its spatial accuracy is still unsatisfied. In the present work, an improved fringe Fourier analysis method is proposed to process the results obtained from the laser interferometry measurement, aiming to accurately determine the spatial distribution of flame heat release rate perturbation. The measurement of heat release rate perturbation was performed on a acoustic perturbed laminar premixed flame, with the burner outlet diameter of 8 mm. Interference patterns generated by two laser beams with a diameter of 70 mm were recorded at a frame rate of 6000 Hz. A spatial dependent fringe processing method, referred as the improved fringe Fourier analysis, was developed to demodulate the interference phase from the fringe patterns. The proper orthogonal decomposition analysis was performed on these results to analyze the component of interference signals. Validation of the present technique was conducted by comparing the heat release rate perturbation field resulting from the laser interferometric technique to those from the CH* chemiluminescence from the flame. Comparisons were performed both for the global and local values, and the low-frequency natural oscillation effects were analyzed. Finally, a refraction correction method based on background-oriented Schlieren is proposed to compensate the beam deflection caused by flame.

Extension of the law of the wall exploiting weak similarity of velocity fluctuations in turbulent channels

This paper explores the similarity of the streamwise velocity fluctuations in turbulent channels. In the analysis, we employ a one-dimensional scalar variant of the proper orthogonal decomposition (POD). This approach naturally motivates the introduction of two different levels of similarity which we will refer to as strong and weak similarity. Strong similarity requires that the two-point correlation and thus, all POD modes, show Reynolds number similarity, while weak similarity only requires that the first few POD modes show similarity. As POD concerns information at more than one location, these similarities are more general than various similarities found in the literature concerning single-point flow statistics. We examine flows at Reτ=180, 540, 1000, and 5200. Strong similarity is observed in the viscous layer and the wake region, and weak similarity is found in both the viscous wall region and the outer part of the logarithmic layer. The presence of weak similarity suggests the existence of an extension to the law of the wall (LoW). We propose such an extension based on the results from the one-dimensional POD analysis. The usefulness of the LoW extension is then assessed by comparing flow reconstructions according to the conventional equilibrium LoW and the extended LoW. We show that the extended LoW provides accurate flow reconstructions in the wall layer, capturing fine-scale motions that are entirely missed by the equilibrium LoW.

Investigation into the Effect of H2-Enriched Conditions on the Structure and Stability of Flames in a Low-Swirl Combustor Derived from Aero-Engine Design

This study introduces an innovative approach involving the injection of hydrogen into a low-swirl, non-premixed flame, which operates with gaseous fuels derived from an air-blast atomizer designed for aero-engine applications. The aim is to characterize how hydrogen enrichment influences flame structures while maintaining a constant thermal output of 4.6 kW. Using high-speed chemiluminescence imaging, three fueling conditions were compared: the first involved pure methane/air, while the second and third conditions introduced varying levels of hydrogen to an air–methane mixture. The results reveal significant effects of hydrogen enrichment on flame characteristics, including a slightly shorter length and a wider angle attributed to heightened expansion within the Combustion Recirculation Zone. Moreover, the emission of UV light underwent considerable changes, resulting in a shifted luminosity zone and reduced variance. To delve deeper into the underlying mechanisms, the researchers employed Proper Orthogonal Decomposition (POD) and Spectral Proper Orthogonal Decomposition (SPOD) analyses, showing coherent structures and energetic modes within the flames. Hydrogen enrichment led to the development of smaller structures near the nozzle exit, accompanied by longitudinal oscillations and vortex shedding phenomena. These findings contribute to an advanced understanding of hydrogen’s impact on flame characteristics, thereby propelling efforts toward improved flame stability. Additionally, these insights hold significance in the exploration of hydrogen as an alternative energy source with potential environmental benefits.

POD Analysis of Flow around Torpedo-Like Geometry with a Hemispherical Nose

There has been an increased interest in underwater vehicles for a wide range of applications over the past decade. In the current study, flow characteristics around a common, torpedo-like geometry with a Myring profile were investigated at a length-based Reynolds number of Re=20000 using the Particle Image Velocimetry (PIV). As a result of PIV and Proper Orthogonal Decomposition (POD) analyzes in this study; instantaneous streamline topology Ψ, instantaneous vorticity ωL⁄U_∞ contours, instantaneous streamwise velocity component u⁄U_∞ graphs, cross-streamwise velocity component v⁄U_∞ graphs, instantaneous vorticity ωL⁄U_∞ graphs, perpendicular to the flow direction, instantaneous vortex graphs and time-averaged TKE graphs were evaluated and compared. At the same time, as a result of PIV analysis, time-average streamline topology <Ψ> and Time-averaged vorticity <ωL⁄U_∞ > contours values are given. When the flow characteristics were compared by using the obtained POD method of the PIV results, it was determined that although the POD data were generally quite similar to the PIV results, the POD analysis results had a more uniform flow structure and vortex turbulence was lessened.

Improved Spatiotemporal Distributions of Sweeping Jet Film Cooling With a Shaped Exit Design

Abstract Sweeping jet (SJ) is a self-excited flow control device that can generate continuous and periodic flow, which makes it a promising geometry for film cooling. However, the cooling performance of current SJ configurations is not significantly better than that of 777-shaped holes. This paper presents two modified SJ configurations, named shaped SJ1 and shaped SJ2, which possess distinct shaped exit geometries. The spatiotemporal coolant distributions were comprehensively quantified for the 777-shaped hole, the compact SJ (with compact geometry), the shaped SJ1, and the shaped SJ2. The instantaneous cooling effectiveness distributions of the four configurations at blowing ratios (M) ranging from 0.5 to 3.0 were measured using the fast pressure-sensitive paint technique. The shaped SJ2 integrated the cooling characteristics of the 777-shaped hole and SJ. It maintained stability at a relatively low M, while began to oscillate when M was increased above 1.5. The shaped SJ design exhibited superior cooling effectiveness at both low and high M of 0.5 to 3.0. A proper orthogonal decomposition analysis and simulations illustrated the oscillation processes and flow structures within the SJ configuration. The shaped SJ2 showed a reduced outlet momentum and a more even distribution of film coverage than the 777-shaped hole, resulting in considerably improved cooling performance.