Backward-facing Step Research Articles

Generative learning for forecasting the dynamics of high-dimensional complex systems

We introduce generative models for accelerating simulations of high-dimensional systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are down sampled to a lower dimensional manifold that is evolved through an auto-regressive attention mechanism. In turn, Bayesian diffusion models, that map this low-dimensional manifold onto its corresponding high-dimensional space, operate on batches of physics correlated, time sequences of data and capture the statistics of the system dynamics. We demonstrate the capabilities and drawbacks of G-LED in simulations of several benchmark systems, including the Kuramoto-Sivashinsky (KS) equation, two-dimensional high Reynolds number flow over a backward-facing step, and simulations of three-dimensional turbulent channel flow. The results demonstrate that generative learning offers new frontiers for the accurate forecasting of the statistical properties of high-dimensional systems at a reduced computational cost.

Experimental control of the flow separation behind a backward facing step using deep reinforcement learning

In this experimental study, a value-based reinforcement learning algorithm (deep Q-network, DQN) is used to control the flow separation behind a backward facing step at a Reynolds number of 2.9 × 104. The flow is forced by a dielectric barrier discharge (DBD) plasma actuator pasted at the upstream of the step edge, and the feedback information of the separation zone is provided by a hotwire sensor submerged in the downstream shear layer. The control law represented by a deep neural network is implemented on a field programable gate array (FPGA), able to execute in real-time at a frequency as high as 1000 Hz. Results show that both open-loop periodical control and DQN control can effectively reduce the reattachment length and the recirculation area. Compared with the former, which requires dozens of trail-and-error measurements lasting for hours, the latter is able to find an optimal control law in only two minutes, achieving a long-term reward 7% higher. Moreover, by introducing a weak penalty term for plasma actuation, the mean actuator power consumption in DQN can be cut down to only 60% of that in the optimal open-loop control, meanwhile sacrificing a negligible amount of control effectiveness. Physically, the open-loop periodical control destabilizes the shear layer earlier, increasing both the area and the peak amplitude of the high turbulent kinetic energy (TKE) zone, whereas under DQN control, only a slight increase in the TKE peak is observed, and the overall spatial distribution remains the same as baseline.

A non-localized spatial–temporal constitutive relation in rarefied gas dynamics

Although the Boltzmann equation is instrumental in capturing the dynamics of rarefied gases, finding its solutions in engineering problems is challenging. Therefore, over the past century and a half, numerous partial differential equations based on a few macroscopic variables have been introduced. However, they not only have complicated forms but also cannot make satisfactory prediction when the Knudsen number is large. Here, we propose a non-localized spatial–temporal (NiST) constitutive relation for rarefied gas dynamics, where the stress/heat flux at time t and position x is determined by the velocity/temperature gradient in the nearby spatial–temporal coordinates, via convolution operators. Utilizing solutions of the Boltzmann equation for the Couette/Fourier/Poiseuille flow and the spontaneous Rayleigh–Brillouin scattering, we extract the universal parameters of non-locality as functions of the spatial and temporal Knudsen numbers. Subsequent validation through sound propagation and backward-facing step flow demonstrates that the NiST constitutive relation is capable of accurately forecasting rarefied gas flows across a broad spectrum of Knudsen numbers.

Numerical Study of High-g Combustion Characteristics in a Channel with Backward-Facing Steps

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.

A Neural Network-Based Poisson Solver for Fluid Simulation

The pressure Poisson equation is usually the most time-consuming problem in fluid simulation. To accelerate its solving process, we propose a deep neural network-based numerical method, termed Deep Residual Iteration Method (DRIM), in this paper. Firstly, the global equation is decomposed into multiple independent tridiagonal sub-equations, and DRIM is capable of solving all the sub-equations simultaneously. Moreover, we employed Residual Network and a correction iteration method to improve the precision of the solution achieved by the neural network in DRIM. The numerical results, including the Poiseuille flow, the backwards-facing step flow, and driven cavity flow, have proven that the numerical precision of DRIM is comparable to that of classic solvers. In these numerical cases, the DRIM-based algorithm is about 2–10 times faster than the conventional method, which indicates that DRIM has promising applications in large-scale problems.

New insights on cavitating flows over a microscale backward-facing step

This study introduces the first experimental analysis of shear cavitation in a microscale backward-facing step (BFS) configuration. It explores shear layer cavitation under various flow conditions in a microfluidic device with a depth of 60 μm and a step height of 400 μm. The BFS configuration, with its unique characteristics of upstream turbulence and post-reattachment pressure recovery, provides a controlled environment for studying shear-induced cavitation without the complexities of other microfluidic geometries. Experiments were conducted across four flow patterns: inception, developing, shedding, and intense shedding, by varying upstream pressure and the Reynolds number. The study highlights key differences between microscale and macroscale shear cavitation, such as the dominant role of surface forces on nuclei distribution, vapor formation, and distinct timescales for phenomena like shedding and shockwave propagation. It is hypothesized that vortex strength in the shear layer plays a significant role in cavity shedding during upstream shockwave propagation. Results indicate that increased pressure notably elevates the mean thickness, length, and intensity within the shear layer. Instantaneous data analysis identified two vortex modes (shedding and wake modes) at the reattachment zone, which significantly affect cavitation shedding frequency and downstream penetration. The wake mode, characterized by stronger and lower-frequency vortices, transports cavities deeper into the channel compared to the shedding mode. Additionally, vortex strength, proportional to the Reynolds number, affects condensation caused by shockwaves. The study confirms that nuclei concentration peaks in the latter half of the shear layer during cavitation inception, aligning with the peak void fraction region.

Effect of flameholding cavity geometry on the flowfield of a solid fuel scramjet

An optically accessible solid fuel scramjet was used to investigate the supersonic combustion of varying polymethyl methacrylate solid fuel grain geometries. The rear wall angle of the flameholding cavity was varied (30, 60, 75, and 90°) and an alternative geometry (flush fuel grain) containing the addition of a backwards facing step to the front of a conventional fuel grain was explored. Optical diagnostics including high-speed shadowgraph, CH* chemiluminescence, and HD video were used to analyze flammability characteristics and determine quantitative regression rates for each geometry. The optical results were supplemented by static pressure traces along the length of the combustor for the duration of a test firing. All tests were conducted with Mach 2 inlet flow into the combustor at nominal inlet conditions of 12.9 atm and 900 °C. Shadowgraph imaging for both cold flow and combusting flow was used to characterize the varying flow fields associated with their respective geometries and their core flow oscillatory frequencies were preliminarily inspected. Chemiluminescence data reveals increased heat release in the downstream constant area and expansion sections of the flush fuel grains compared to conventional geometries. This heat release appears to correlate with increased time-averaged regression rates in these regions while the varying cavity angle fuel grains demonstrate differing magnitudes of maximum regression along the rear cavity wall and onset of the constant area section. In addition to increased overall regression rates, flush geometries increase the flameholding capabilities and demonstrate self-sustained burning at lower inlet temperatures than similar geometries designed without a flush section.

Large-Eddy Simulation Study of Flow and Combustion Dynamics in a Full-Scale Hydrogen-Air Rotating Detonation Combustor-Stator Integrated System

Abstract A first-of-its-kind large-eddy simulation (LES) study is conducted to numerically investigate the combustion dynamics as well as aero-thermal phenomena in a full-scale non-premixed hydrogen-air rotating detonation engine (RDE) integrated with nozzle guide vanes (NGV) acting as the turbine stator. The LES framework incorporates hydrogen-air detailed chemical kinetics and adaptive mesh refinement. A comparative analysis is carried out for two operating conditions with different fuel/air mass flow rates but global equivalence ratio of unity. The LES model is validated against experimental data with respect to detonation wave speed/height, wave dynamics, and axial static pressure distribution. Numerical results indicate significant deflagrative combustion occurring in the fill region near the inner wall due to formation of recirculation zones in the injection near-field driven by the backward facing step. The leading detonation wave is found to be trailed by an azimuthal reflected-shock combustion wave, which consumes unburned vitiated reactants that leak through the main detonation wave. The detonation wave characteristics do not change appreciably with the presence of NGV. The exit flow is found to be nearly fully subsonic and supersonic for the low and high mass flux conditions, respectively. The presence of NGV renders the flow more axial, and significantly impacts the exit Mach number and total pressure. The low mass flux operating point, despite exhibiting more deflagrative losses within the combustor, yields overall lower pressure drop from plenum to exhaust, mainly attributed to lower pressure drop across the injectors.

محاكاة تدفق السوائل النانوية الصفائحية على خطوة ساخنة مزدوجة مواجهة للخلف

This research focuses on heat transfer enhancement by separating flow over a double backward-facing step using nanofluid. To conduct this research, a numerical model was constructed using the ANSYS Workbench, and the governing equations were solved using the realizable k-ε model with a second-order upwind scheme. Three different types of base fluid (water, engine oil, and ethylene glycol) with nanoparticles (AL2O3, TiO2, and Cu) were used for Reynolds numbers ranging from 200 to 1000. The constant heat flux of the 2000 W/m2 boundary condition is considered on the lower wall. The effect of nanoparticle material, nanoparticle concentrations, nanoparticle sizes, and Reynolds numbers on the Nusselt number is investigated. Two different approaches for estimating nanofluid thermal conductivity and viscosity have been used. The numerical code results were verified with previous numerical data. The results showed that the peak of the Nusselt number occurs immediately after the steps. The results demonstrated a significant improvement in the heat transfer performance of nanofluids, especially Cu/engine oil nanofluids, compared to conventional base fluids with other nanoparticles. It was noticed that the Nusselt number increases with decreasing nanoparticle diameter and also with increasing Reynolds number.

Reynolds-Number-Dependence of Length Scales Governing Turbulent-Flow Separation in Wall-Modeled Large Eddy Simulation

This paper proposes a Reynolds number Re scaling for the number of grid points Ncv required in wall-modeled Large Eddy Simulation (WMLES) of turbulent boundary layers (TBL) to accurately capture the regions of flow separation. Based on the various time scales in a nonequilibrium TBL, a definition of the near-wall “underequilibrium” scales is proposed (in which “equilibrium” refers to a quasi balance between the viscous and the pressure gradient terms). This length scale is shown to vary with Reynolds number as lp∼Re−2/3. A-priori analysis demonstrates that the resolution (Δ) required to reasonably predict the wall stress in several nonequilibrium flows is at least O(10)lp, irrespective of the Reynolds number and Clauser parameter. Further, a-posteriori studies (on the Boeing speed bump, Song– Eaton diffuser, Notre-Dame Ramp, and the backward-facing step) show that scaling Δ such that Δ/lp is independent of Reynolds number results in accurate predictions of separation for the same “nominal” grid across different Reynolds numbers. Finally, we suggest that near separation and reattachment points, Ncv for WMLES scale as Re4/3, which is more restrictive than the previous estimates (∼Re1) by Choi and Moin (Choi, H., and Moin, P., “Grid-Point Requirements for Large Eddy Simulation: Chapman’s Estimates Revisited,” Physics of Fluids, Vol. 24, No. 1, 2012, Paper 011702) and Yang and Griffin (Yang, X. I. A., and Griffin, K. P., “Grid-Point and Time-Step Requirements for Direct Numerical Simulation and Large-Eddy Simulation,” Physics of Fluids, Vol. 33, No. 1, 2021, Paper 015108).

Numerical Analysis of Heat Transfer Enhancement Using Water / FMWCNT Nanofluid Passed in a 2D Backward Facing Step Channel

Numerical Analysis of Heat Transfer Enhancement Using Water / FMWCNT Nanofluid Passed in a 2D Backward Facing Step Channel

Dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor.

We numerically study the dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor using analytical methodologies based on dynamical systems theory, symbolic dynamics, complex networks, and machine learning. The global dynamic behavior of a heat release rate field represents low-dimensional chaotic oscillations with deterministically aperiodic intercycle dynamics. Spray combustion instability is driven in the formation and separation region of a large-scale organized vortex induced by the hydrodynamic shear layer instability at the edge of the backstep. This region corresponds fairly to that of the hub in an acoustic-energy-flux-based spatial network. The feature importance in a random forest is valid for clarifying the feedback coupling of spray combustion instability.

Numerical Study of Magnetohydrodynamic Forced Convective Nanoliquid Flow Through a Channel with Backward Facing Step and Three Hot Cylinder Blocks

Numerical Study of Magnetohydrodynamic Forced Convective Nanoliquid Flow Through a Channel with Backward Facing Step and Three Hot Cylinder Blocks

Identifying optimal location for control of thermoacoustic instability through statistical analysis of saddle point trajectories.

We propose a framework of Lagrangian Coherent Structures (LCSs) to enable passive open-loop control of tonal sound generated during thermoacoustic instability. Experiments were performed in a laboratory-scale bluff-body stabilized turbulent combustor in the state of thermoacoustic instability. We use dynamic mode decomposition on the flow-field to identify dynamical regions where the acoustic frequency is dominant. We find that the separating shear layer from the backward-facing step of the combustor envelops a cylindrical vortex in the outer recirculation zone, which eventually impinges on the top wall of the combustor during thermoacoustic instability. We track the saddle points in this shear layer emerging from the backward-facing step over several acoustic cycles. A passive control strategy is then developed by injecting a steady stream of secondary air targeting the identified optimal location where the saddle points spend a majority of their time in a statistical sense. After implementing the control action, the resultant flow-field is also analyzed using LCS to understand the key differences in flow dynamics. We find that the shear layer emerging from the dump plane is deflected in a direction almost parallel to the axis of the combustor after the control action. This deflection, in turn, prevents the shear layer from enveloping the vortex and impinging on the combustor walls, resulting in a drastic reduction in the amplitude of the sound produced.

Low-frequency dynamics of turbulent recirculation bubbles

We revisit the origin of low-frequency unsteadiness in turbulent recirculation bubbles (TRBs), and, in particular, the hypothesis of a dynamic feedback mechanism between unconstrained separation and reattachment locations. To this end, we conduct wall-resolved large-eddy simulations of a novel experimental configuration where a shock-induced TRB forms over a backward-facing step that is intended to intercept the hypothesized dynamic feedback. Our results demonstrate, for the first time, effective suppression of the low-frequency characteristics of the TRB without reducing its size, strongly supporting our hypothesis.

The loss mechanisms and vortex dynamics of rotor platform step geometries in a low-speed research compressor stage

The construction and assembly of an axial compressor blade row introduces real geometric features, which leads to the deviation of flow characteristics from the intended design. According to the realistic assembly errors observed in the four-stage low-speed research compressor developed by Shanghai Jiao Tong University, two representative step geometries at the rotor platform were abstracted. Unsteady simulations were carried out in the stage environment to study the influence of hub discontinuities on compressor performance and loss mechanisms. The comparisons of smooth hub, elevated hub (EH), and a wedged hub (WH) demonstrated that all the step geometries resulted in increased loss inside both rotor and stator rows. The loss induced by WH was more sensitive to step heights than EH. Under the influence of forward facing step, rotor incidence was reduced and horseshoe vortex (HV) was exacerbated, leading to the accumulation and separation of low momentum fluids at the pressure side corner. This led to a redistribution of losses across the span. In the lower half span, the relative total pressure loss increased almost linearly with step heights, while in the tip region, it reduced slightly. The backward facing step generated the step corner vortices (SCV) that shed and propagated downstream. The SCV interacted with the HV and cavity leakage vortex in the stator passage. Coupled with the augmented stator inflow angle, the corner separation at the suction side was dramatically intensified and led to a significant loss increase.

Reconstruction of the turbulent flow field with sparse measurements using physics-informed neural network

Accurate high-resolution flow field prediction based on limited experimental data is a complex task. This research introduces an innovative framework leveraging physics-informed neural network (PINN) to reconstruct high-resolution flow fields using sparse particle image velocimetry measurements for flow over a periodic hill and high-fidelity computational fluid dynamics data for flow over a curved backward-facing step. Model training utilized mean flow measurements, with increased measurement sparsity achieved through various curation strategies. The resulting flow field reconstruction demonstrated marginal error in both test cases, showcasing the ability of the framework to reconstruct the flow field with limited measurement data accurately. Additionally, the study successfully predicted flow fields under two different noise levels, closely aligning with experimental and high-fidelity results (experimental, direct numerical simulation, or large eddy simulation) for both cases. Hyperparameter tuning conducted on the periodic hill case has been applied to the curved backward-facing step case. This research underscores the potential of PINN as an emerging method for turbulent flow field prediction via data assimilation, offering reduced computational costs even with sparse, noisy measurements.

Effect of incoming flow conditions on air lubrication regimes

Different air phase regimes are formed by controlled air injection in a spatially developing flat plate turbulent boundary layer (TBL). The air is introduced via a slot type injector without the use of a backward-facing step or cavitator upstream of the air injection position. The effect of different incoming liquid flow characteristics on the different regimes is investigated by varying both the liquid freestream velocity and the incoming TBL thickness. The latter is realized through changing the position of the air injection along the length of the water tunnel facility. That resulted in a downstream distance based Reynolds number from 1 to 5 million. Three different air phase regimes are identified under different air flow rates and freestream velocities: the bubbly regime, the transitional, and the air layer regime. The morphological differences of each one are described and quantitative analysis is performed based on the non-wetted area in each condition. The incoming TBL as well as the flow around the air layer are measured with planar particle image velocimetry. The latter enabled the determination of the air layer thickness. In addition, the ratio of the air layer to the incoming boundary layer thickness tair/δ is also calculated (≈ 0.04 – 0.5). This is a significant dimensionless parameter for scaling, which indicates the extent to which the air layer is embedded within the incoming TBL. Depending on the incoming flow conditions, a two or three branch air layer is formed. The length of the air layer is found to increase with increasing liquid freestream velocities. A good agreement between the air layer length and a half gravity wave predicted by the dispersion relation is found. An increase of the air layer length is observed with a decreasing incoming TBL thickness. This is attributed to a decrease in the local mean velocity at the air–water interface due to the TBL growth. Finally, increasing the incoming TBL thickness delays the onset of the air layer regime.

Growth of organized flow coherent motions within a single-stream shear layer: 4D-PTV measurements

This study investigates the evolution of a single-stream shear layer (SSSL) originating from a wall boundary layer past a backward-facing step. Utilizing a time-resolved 3D-Particle Tracking Velocimetry (4D-PTV) technique, we track the trajectories of fluorescent particles to gain insight into the flow characteristics of the SSSL. A compact water tunnel facility (Reτ=1240\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{Re}_\ au =1\\,240$$\\end{document}) is fabricated to obtain an SSSL with a perpendicular slow entrainment stream past the separation edge. A hybrid interpolation approach that combines ensemble binning and Gaussian weighting is implemented to derive minimally filtered mean and instantaneous lower- and higher-order flow field parameters. Spanwise-dominant coherent motion accompanied by finer flow scales is observed to grow due to flow entrainment through “nibbling” actions of small-scale vortices, “engulfing” by large-scale vortices, and vortex pairing events. Furthermore, the non-zero-speed stream edge grows relatively faster than the zero-speed stream edge, showing a strong asymmetry in mixing composition across a mixing layer. The SSSL reaches self-similarity at a streamwise distance of ≈55θ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\approx 55\\,\ heta _{0}$$\\end{document}, where θ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _0$$\\end{document} is the initial momentum thickness from the separation edge, i.e., considerably shorter than reported in previous studies. A literature comparison of growth rate parameters raises intriguing questions regarding a potential inclusive growth scaling unifying the free shear layers. A turbulent kinetic energy (TKE) budget analysis reveals a negative production region immediately downstream of the separation edge attributed to a large positive streamwise gradient of streamwise velocity. In the self-similar region, the phase-averaged flow mapping demonstrates a larger concentration of turbulence production rate around the outer edges of spanwise vortices, specifically at the intersection of braids and vortices. Furthermore, a spatial separation exists in the regions of peak production and dissipation rates within the vortex core region favoring dissipation. The braids exhibit a larger concentration of turbulence diffusion rates, indicating their function as a conduit for exchanging turbulence between neighboring coherent motions.

Towards High-Speed And High-Resolution Real-Time Optical Flow Particle Image Velocimetry

One of the major advantages of Optical Flow PIV (Particle Image Velocimetry) algorithms over Cross-Correlation PIV is their scalability leading to potentially very high computational speeds. This is confirmed in this study using different GPUs (Graphics Processor Unit) and different image sizes. The other advantage is the possibility of obtaining dense velocity fields of up to one vector per pixel. It is well known that particle seeding plays a crucial role in the results of standard particle image velocimetry based on cross-correlation algorithms. Its influence on the quality of the optical flow algorithm is not as well established. In this article the influence of particle concentration is quantified by introducing a criterion considering the proportion of “active” pixels in a snapshot. It is shown that it is possible to optimize particle concentration to maximize the percentage of active pixels, leading to better spatial resolution, down to one vector per pixel. The principle is validated on a vortex-free flow and applied to the complex 3D flow downstream a backward-facing step.