Search Results (64)

This tutorial takes the reader on a historical and technical journey from the simple Perceptron (1958) to modern Convolutional Neural Networks (CNNs) that dominate spatial data processing (images and video). We start with the Perceptron’s linear classifier, then expose its inability to learn non-linear patterns (e.g., XOR), which motivates the Multi-Layer Perceptron (MLP) and the backpropagation algorithm. Next, we discuss the limitations of MLP when faced with structured data like images—parameter explosion, loss of spatial information, and lack of translation invariance—and use these limitations as a natural springboard to the core ideas of CNNs: local connectivity, weight sharing, and hierarchical feature learning. Throughout, we provide intuitive explanations, mathematical formulations, and step-by-step numerical examples (e.g., a complete forward and backward pass for a small network, and a manual 2D convolution). Clear graphical representations and examples help readers understand each concept. The tutorial concludes with a detailed walkthrough of influential CNN architectures (LeNet-5, AlexNet, VGG, GoogLeNet, ResNet, DenseNet, and EfficientNet) and also discusses more recent attention-based models (e.g., Vision Transformers and ConvNeXt), explaining why each was necessary and how it advanced the field. Aimed at students and practitioners with a basic knowledge of calculus and linear algebra, this tutorial connects foundational ideas to state-of-the-art deep learning, focusing on spatial data. It is designed for readers who want to understand why each architectural choice was made, not just what the final model looks like. Full article

This study investigates the passive control of backward-facing step flows using rigid and elastic cantilevered plates, with emphasis on flow reattachment, pressure recovery, and fluid–structure interaction effects. The numerical methodology was first validated against an experimental benchmark, yielding a reattachment-length prediction within 1.28% of the measured value. Following validation, simulations were performed using the unsteady Reynolds-averaged Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model. Rigid plate configurations were examined at momentum-thickness-based Reynolds numbers of $R{e}_{\theta }=500$, 1000, and 5000, while two-way fluid–structure interaction simulations were conducted at $R{e}_{\theta }=5000$ to evaluate the influence of structural stiffness. For the baseline configuration, the non-dimensional reattachment length and base drag coefficient remained within the ranges of $x_r/h=6.18$–$6.34$ and $c_B=0.199$–$0.205$, respectively. The most effective rigid configuration, $L/h=2.5$, reduced the reattachment length from $x_r/h=6.34$ to $x_r/h=5.57$ and the base drag coefficient from $c_B=0.205$ to $c_B=0.175$ at $R{e}_{\theta }=5000$, corresponding to reductions of approximately 12% and 15%, respectively. The fluid–structure interaction simulations showed that plate stiffness strongly influences flow-control effectiveness. The stiffest elastic configuration, with $E=2\times {10}^9$ Pa, achieved $x_r/h=6.14$ and $c_B=0.196$, whereas more flexible plates exhibited larger deformation and reduced aerodynamic benefit. Overall, the results demonstrate that cantilevered plates provide an effective passive flow-control strategy for backward-facing step flows. Rigid plates deliver the greatest aerodynamic improvement, while elastic plates require sufficient structural stiffness to maintain favorable pressure recovery and flow-reattachment characteristics. Full article

Understanding and modeling the effect of magnetic fields on flows that present separation properties, such as those over a backward-facing step (BFS), is critical due to its role in metallurgical processes, nuclear reactor cooling, plasma confinement, and biomedical applications. This study examines the hydrodynamic and magnetohydrodynamic numerical solution of an electrically conducting fluid flow in a backward-facing step (BFS) geometry under the influence of an external, uniform magnetic field applied at an angle. The novelty of this work lies in employing an in-house finite-volume solver with a collocated grid configuration that directly applies a Newton–like method, in contrast to conventional iterative approaches. The computed hydrodynamic results are validated with experimental and numerical studies for an expansion ratio of two, while the MHD case is validated for Reynolds number $Re=380$ and Stuart number $N=0.1$. One of the most important findings is the reduction in the reattachment point and simultaneous increase in pressure as the magnetic field strength is amplified. The magnetic field angle with the greatest influence is observed at $\phi =\pi /2$, where the main recirculation vortex is substantially suppressed. These results not only clarify the role of magnetic field orientation in BFS flows but also lay the foundation for future investigations of three-dimensional configurations and coupled MHD–thermal applications. Full article

Accurately identifying coherent vortex structures (CVSs) in backward-facing step (BFS) flows remains a challenge, particularly in reconciling visual streamlines with mathematical criteria. In this study, high-resolution velocity fields were captured using particle image velocimetry (PIV) in a pressurized BFS setup. Instantaneous streamlines reveal distinct spiral patterns, vortex centers, and saddle points, consistent with physical definitions of vortices and offering intuitive guidance for CVS detection. However, conventional vortex identification methods often fail to reproduce these visual features. To address this, an improved Q-criterion method is proposed, based on the normalization of the velocity gradient tensor. This approach enhances the rotational contribution while suppressing shear effects, leading to improved agreement in vortex position and shape with those observed in streamlines. While the normalization process alters the representation of physical vortex strength, the method bridges qualitative visualization and quantitative analysis. This streamline-consistent identification framework facilitates robust CVS detection in separated flows and supports further investigations in vortex dynamics and turbulence control. Full article

Curved surfaces are a feature of many engineering applications, and as such, the accurate prediction of separation and reattachment from a curved surface is of great engineering importance. In this study, improved delayed detached eddy simulation (IDDES) is used, in conjunction with synthetic turbulence injection using the synthetic eddy method (SEM), to investigate the boundary layer separation from a curved backward-facing step for which large eddy simulation (LES) results are available. The commercial code Star CCM+ was used with the k-ω shear stress transport (SST) variation of the IDDES model to assess the accuracy of the code for this class of problem. The IDDES model predicted the separation length within 10.4% of the LES value for the finest mesh and 25.5% for the coarsest mesh, compared to 36.2% for the RANS simulation. Good agreement between the IDDES and LES was also found in terms of the distribution of skin friction, velocity, and Reynolds stress, demonstrating an acceptable level of accuracy, as has the prediction of the separation and reattachment location. The model has, however, found it difficult to capture the pressure coefficient accurately in the region of separation and reattachment. Overall, the IDDES model has performed well against a type of geometry that is typically a challenge to the hybrid RANS-LES method (HRLM). Full article

A time-consistent upwind difference scheme with a preconditioned numerical flux for unsteady gas-liquid multiphase flows is presented and applied to the analysis of cavitating flows. The fundamental equations were formulated in general curvilinear coordinates to apply to diverse flow fields. The preconditioning technique was applied specifically to the numerical dissipation terms in the upwinding process without changing the time derivative terms to maintain time consistency. This approach enhances numerical stability in unsteady multiphase flow computations, consistently delivering time-accurate solutions compared to conventional preconditioning methods. A homogeneous gas-liquid two-phase flow model, third-order Runge-Kutta method, and the flux difference splitting upwind scheme coupled with a third-order MUSCL TVD scheme were employed. Numerical tests of two-dimensional gas-liquid single- and two-phase flows over backward-facing step with different step height and flow conditions successfully demonstrated the capability of the present scheme. The calculations remained stable even for flows with a very low Mach number of 0.001, typically considered incompressible flows, and the results were in good agreement with the experimental data. In addition, we analyzed unsteady cavitating flows at high Reynolds numbers and confirmed the effectiveness and applicability of the present scheme for calculating unsteady gas-liquid two-phase flows. Full article

Numerical investigations were conducted to analyze the coupling effects of pulsed H₂ jets and nanosecond-pulsed actuation (NS-SDBD) in a supersonic crossflow. The FVM was employed to solve the multi-component 2D URANS equations with the SST k-omega turbulence model, while H₂-air combustion was described using a seven species–seven reactions chain reaction model, and the plasma thermal effect was represented by a phenomenological model. The backward-facing step flows with an inlet Mach number of 2.5 and a pulsed jet frequency of 10 kHz under different actuation conditions were simulated. The combustion enhancement mechanism under an actuation frequency of 20 kHz was analyzed. Research indicates that compression waves induced by NS-SDBD enhance H₂-air mixing and facilitate temperature transport as the flow progresses. This progress is significantly associated with the flow structures generated by pulsed jets. Under this condition, the fuel utilization rate in the flow field increased by 61.2%, the total pressure recovery coefficient increased by 5.34%, and the outlet total temperature slightly increased even with a 50% reduction in fuel flow rate. Comparative analysis of different actuation cases demonstrates that evenly distributed actuation within the jet cycle yields better effects. The innovation of this study lies in proposing and exploring a potential method to address inadequate combustion under high-speed inflow conditions, which couples NS-SDBD with pulsed hydrogen jets. Full article

High gravity (high-g) combustion can significantly increase flame propagation speed, thereby potentially shortening the axial length of aero-engines and increasing their thrust-to-weight ratio. In this study, we utilized the large eddy simulation model to investigate the combustion characteristics and flame morphology evolution of premixed propane–air flames in a channel with a backward-facing step. The study reveals that both the increase in centrifugal force and flow velocity can enhance pressure fluctuations during combustion and increase the turbulence intensity. The presence of centrifugal force promotes the occurrence of Rayleigh–Taylor instability (RTI) between hot and cold fluids. The combined effects of RTI and Kelvin–Helmholtz instability (KHI) enhance the disturbance between hot and cold fluids, shorten the fuel combustion time, and intensify the dissipation of large-scale vortices. The increase in fluid flow velocity can raise the flame front’s hydrodynamic stretch rate, thereby enhancing the turbulence level during combustion to a certain extent and increasing the fuel consumption rate. When a strong centrifugal force is applied, the global flame propagation speed can be more than doubled. Within a certain range, the increase in high-g field strength can enhance the intensity of RTI and accelerate the transition of RTI to the nonlinear stage. Full article

Laminar flow over a modified backward-facing step (BFS) was studied experimentally and computationally, with the results compared to a flight test on a Piper Cherokee wing. The BFS was modified with a serrated spanwise variation while maintaining a constant step height, and this modification is termed a serrated BFS (sBFS). A scaling law was proposed and then used to develop the experimental operation conditions. The experiments showed evidence that the transition to turbulence was delayed over the forward part of the serration (termed the valley). The boundary layer growth and characterization were used to validate the computational model, which was then used to examine details not available from the experiment, including the wall shear stress distribution and streamlines as they go over the sBFS. The wall shear stress showed the formation of low-shear diamonds downstream of the sBFS valley that were associated with laminar flow, which confirmed previous assumptions about the low-shear diamonds observed in the flight tests. The length of the low-shear diamonds was scaled with the sBFS geometry. Finally, the streamlines showed that the near-wall flow forward of the sBFS is pumped towards the sBFS peak, where it rapidly transitions to turbulence at that location. Full article

Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward-facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers are generated. Curved free shear layer flows, however, have not received sufficient attention, especially in the nonlinear regime. The present work investigates the development of centrifugal instabilities in a curved free shear layer flow in the nonlinear compressible regime. The compressible Navier–Stokes equations are reduced to the nonlinear boundary region equations (BREs) in a high Reynolds number asymptotic framework, wherein the streamwise wavelength of the disturbances is assumed to be much larger than the spanwise and wall-normal counterparts. We study the effect of the freestream Mach number $M_{\infty }$, the shear layer thickness $\delta$, the amplitude of the incoming disturbance A, and the relative velocity difference across the shear layer $\Delta V$ on the development of these centrifugal instabilities. Our parametric study shows that, among other things, the kinetic energy of the curved shear layer flow increases with increasing $\Delta V$ and A decreases with increasing $delta$. It was also found that increasing the disturbance amplitude of the incoming disturbance leads to significant growth in the mushroom-like structure’s amplitude and renders the secondary instability structures more prominent, indicating increased mixing for all Mach numbers under consideration. Full article

The aim of this research work was to explore how modifying the design of small-scale HAWT rotor blades through the backward-facing step technique affects their efficiency under varying wind speeds. The study involved altering step parameters such as location, length, and depth to create four distinct stepped blade shapes and enhance the aerodynamic performance of a rotor with a diameter of 280 mm. A specific blade profile, NREL S822, was selected to meet both aerodynamic and structural criteria. The rotor models were examined at a Reynolds number of 4.7 × 10⁴ for wind speeds between 8.5 and 15.5 m/s and tip-speed ratios between 2 and 5. The experimental results indicated that for certain geometric step parameter values, the efficiency of the rotor model (B3) increased by approximately 47% compared to the base model (B1), particularly for tip-speed ratios lower than around 3.2. However, beyond this point, the rotor efficiency dropped significantly, reaching approximately 60% in one case. Additionally, a hybrid rotor model (B6) was generated by combining the shape of the rotor model (B4) with the most efficient rotor model from the literature, generated using the leading-edge wavy shape technique. This hybrid rotor model enhanced rotor efficiency for specific values of tip-speed ratio and also ensured its smoother operation. Overall, the rotor model (B2), distinguished by smaller step parameter values and a shift as well as broadening of the power coefficient curve towards lower tip-speed ratio values, exhibited a higher peak power coefficient, approximately 1.4% greater than the base rotor (B1). This increase occurred at a lower tip-speed ratio, allowing the rotor to operate with higher efficiency across a broader range of tip-speed ratios. Full article

Multi-person pose tracking is a challenging task. It requires identifying the human poses in each frame and matching them across time. This task still faces two main challenges. Firstly, sudden camera zooming and drastic pose changes between adjacent frames may result in mismatched poses between them. Secondly, the time relationships modeled by most existing methods provide insufficient information in scenarios with long-term occlusion. In this paper, to address the first challenge, we propagate the bounding boxes of the current frame to the previous frame for pose estimation, and match the estimated results with the previous ones, which we call the Backward Temporal Pose-Matching (BTPM) module. To solve the second challenge, we design an Association Across Multiple Frames (AAMF) module that utilizes long-term temporal relationships to supplement tracking information lost in the previous frames as a Re-identification (Re-id) technique. Specifically, we select keyframes with a fixed step size in the videos and label other frames as general frames. In the keyframes, we use the BTPM module and the AAMF module to perform tracking. In the general frames, we propagate poses in the previous frame to the current frame for pose estimation and association, which we call the Forward Temporal Pose-Matching (FTPM) module. If the pose association fails, the current frame will be set as a keyframe, and tracking will be re-performed. In the PoseTrack 2018 benchmark tests, our method shows significant improvements over the baseline methods, with improvements of 2.1 and 1.1 in mean Average Precision (mAP) and Multi-Object Tracking Accuracy (MOTA), respectively. Full article

Backward-facing steps are commonly formed on wings and blades due to misalignment between segments or the addition of protective films. A backward-facing step (BFS) is known to degrade the airfoil performance. To mitigate these adverse effects, a three-dimensional low-profile serrated pattern (termed sBFS) was applied downstream of a BFS on an LA203A profile airfoil. The model drag was determined from wake surveys using a traversing Pitot-static probe within a subsonic wind tunnel operating at a chord-based Reynolds number of 300,000. The airfoil spanned the wind tunnel width (914 mm) and had a 197 mm chord length. Four different sBFS configurations were tested, each formed by applying a 1 mm thick film around the model leading edge. In addition, a BFS at various chord locations and a clean wing (i.e., no film applied) were tested for reference. The sBFS was able to reduce the drag relative the BFS by up to 8–10%, though not outperforming the clean wing configuration. In addition, the wake surveys showed the sBFS produced strong coherent structures that persist into the far-wake region (five chord length downstream of the model) with a scale that was much larger than the step height. Additionally, a computational study was carried out to further examine the flow behavior on the airfoil that produced the coherent structures. This showed that fluid near the surface gets entrained towards the sBFS downstream tip of the sBFS, which creates the initial rotation of these coherent structures that persist into the far-wake region. Full article

This study employs numerical simulations using the combined control volume finite element method (CVFEM) to analyze 2D steady, incompressible laminar flow over a microscale backward facing step within a horizontal duct. The investigation focuses on the impact of Reynolds number (Re_d) and expansion ratio (ER) on flow behavior, aiming to assess the applicability of conventional hydrodynamics at the microscale. The findings reveal that, for an expansion ratio of 2, the flow structure transforms progressively with varying Reynolds numbers in both laminar and transitional flow regimes. Notably, three recirculation zones develop downstream of the step, two along the lower wall and one along the upper wall. The primary recirculation zone's size expands as Reynolds number increases, contracting when a third recirculation zone emerges on the lower wall (Re_d ≥ 950). The study successfully matches its numerical predictions with experimental observations from larger-scale backward-facing steps for Reynolds numbers up to 500, maintaining two-dimensional flow characteristics. Furthermore, the computed velocity profiles align closely with experimental outcomes, except for Re_d = 1000, where the experimental flow shifts to three-dimensionality. The study also examines loss coefficients (Ke), revealing substantially higher values than conventional macro systems for Reynolds numbers above 200. However, for lower Reynolds numbers, the loss coefficient varies accordingly. For expansion ratios of 1.5, 2.0, and 2.5, fluid flow properties such as pressure, Poiseuille number, and friction factors exhibit good agreement with macroscale theory for fully developed laminar flow (Re_d ≤ 500). Full article

This paper presents the flow and flame characteristics of a highly turbulent reactive flow over a backward-facing step inside a windowed combustor. Flow and combustion experiments were performed at Re = 15,000 and Re = 30,000 using high-resolution 10 kHz PIV and 10 kHz PLIF diagnostic techniques. Grid turbulators (Grid) with two different hole diameters (HD of 1.5 mm and 3 mm) and blockage ratios (BR of 46%, 48%, 62%, and 63%) were considered for the turbulence study. Grids introduced different turbulent length scales (L_T) in the flow, causing the small eddies and turbulence intensity to increase downstream. The backward-facing step increased the turbulence level in the recirculation zone. This helped to anchor the flame in that zone. The small HD grids (Grids 1 and 3) produced continuous fluid structures (small-scale), whereas the larger HD grids (Grids 2 and 4) produced large-scale fluid structures. Consequently, the velocity fluctuation was lower (~25.6 m/s) under small HD grids and higher (~27.7 m/s) under large HD grids. The flame study was performed at Φ = 0.8, 1.0, and 1.2 using C-X CH PLIF. An Adaptive MATLAB-based flame imaging scheme has been developed for turbulent reacting flows. Grids 1 and 3 induced more wrinkles in the flame due to higher thermal instabilities, pressure fluctuation, and diffusion under those grids. The flamelet breakdown and burnout events were higher under Grids 2 and 4 due to higher thermal diffusivity and a slower diffusion rate. It was observed that the flame wrinkling and flame stretching are higher at Re = 30,000 compared to Re = 15,000. The Borghi–Peters diagram showed that the flames were within the thin reaction zone except for Grid 1 at Re = 15,000, where flames fell in the corrugated zone. It was observed from PIV and PLIF analyses that Re and L_T mostly controlled the flame and flow characteristics. Full article