Backward-facing Step Research Articles

A novel technique of heat transfer enhancement in backward-facing step flow using a flapping vortex generator

A novel technique of heat transfer enhancement in backward-facing step flow using a flapping vortex generator

Water surface response to turbulent flow over a backward-facing step

The water surface response to subcritical turbulent flow over a backward-facing step (BFS) is studied via high-resolution large-eddy simulation (LES). The LES method is validated first using data of previously reported experiments. The LES-predicted water surface is decomposed into different types of gravity waves as well as turbulence-driven forced waves. Analysis of the LES data reveals the interplay between low-frequency large-scale turbulence structures, which are the result of flow separation from the step and reattachment behind the step, and the dynamics of the water surface. The water surface deformation is mainly the result of freely propagating gravity waves and forced waves, owing to turbulence in the form of rollers and/or hairpin vortices. Gravity waves with zero group velocity define the characteristic spatial and temporal scales of the surface deformations at higher frequencies, while large eddies determine their low-frequency modulation. These deformations are mainly confined in lateral bands that propagate downstream following the advection of the near-surface streamwise vortices (rollers) that are shed from the step. Steeper surface waves are observed in regions of negative perturbation velocity gradient and down-welling, downstream of the larger rollers, and are associated with thin isolated regions of high vorticity near the surface. The investigation of such a complex flow has shown that the decomposition of the water surface fluctuations into its different physical components may be used to identify the dynamics of the underlying flow structure.

Numerical investigation of thermal performance of hydrogen fueled micro-combustor with trapezoidal ribs

This paper presents a new micro combustor design based on four trapezoidal ribs equidistant distributed on its inner wall. The aim is to highlight its promising thermal performance improvements, using numerical simulations as a tool of investigation, compared to other micro combustors. The achieved improvement reflected the favorable effect of the trapezoidal ribs through quantitative computation of mean temperature, temperature difference, and standard deviation. The hydrodynamic study shows that the ribs shape and height elongate the equidistant distributed recirculation zones, resulting in a significant increase in the flow residence time. Furthermore, the outer wall temperature level increases significantly from 1371.25 K to 1417.71 K and the non-uniformity zone is reduced compared to the simple backward facing step micro combustor. A better understanding of the mechanisms involved in heat transfer and their respective contributions to the overall thermal performance of the different micro combustors are explicitly analyzed. Moreover, the results highlight the favorable effect of the inlet velocity of 10 m/s to obtain the optimal outer wall temperature level and uniformity. The rich mixture composition provides the closest thermal performance to the stochiometric case, which widens the operating range for MTPV systems and improves their efficiency and reliability.

Aeroacoustics of turbulent flow over a forward–backward facing step

This paper presents a combined experimental and numerical study on the aeroacoustics of low Mach number turbulent flow over a forward–backward facing step (FBS). The height of the step is fixed at 50% of the incoming boundary layer thickness. Multiple lengths of the step are considered with aspect ratios (step length to height) equal to 1,2,2.4,4, and 8. The Reynolds number based on the step height ranges from 1.2×104 to 2.8×104 in both experiments and simulations. Wall pressure measurement results show that the largest wall pressure fluctuations occur slightly downstream of the step leading edge, and the downstream flow field is influenced by the leading edge flow disturbance. Large-Eddy Simulation (LES) is performed to visualize the instantaneous and time-averaged flow field. Large-scale vortices formed at the leading edge are found to shed downstream directly when the step length is shorter than the shear layer reattachment length, which leads to lower level wall pressure fluctuations on the top surface. Spectral proper orthogonal decomposition (SPOD) is applied to identify the dynamic behaviours of coherent structures downstream of the step leading edge. Using simulation data, the fluctuating wall pressure spectra are also calculated via Poisson’s equation. The results indicate that both turbulence-mean-shear interaction and turbulence–turbulence interaction contribute to the wall pressure fluctuations in the on-step reattachment region. Aeroacoustic beamforming results show that the dominant noise source is located at the step leading edge, where the highest level of fluctuating wall pressure is recorded. Meanwhile, the integrated far-field acoustic spectra show that the levels of FBS noise are lower when there is no flow reattachment occurring on the top surface. A new scaling law for FBS sound spectra is proposed to address the influence of the step aspect ratio on noise production.

Numerical Investigation of Fluid Flow and Heat Transfer Characteristics over Double Backward-Facing Step with Obstacles

Many engineering device, including nuclear reactors, heat exchangers, and electronic circuit boards, exhibit flow separation and reattachment. To reduce thermal stress impacts, the components of these devices, which resemble stepped channel designs and are susceptible to high heat flux, must be properly cooled. The present work numerically investigates the fluid flow and heat transfer characteristics through a double backward-facing step with elliptic obstacles located after each step. For this purpose, equations governing fluid flow and heat transfer are solved in a Cartesian framework using an in-house code based on streamline upwind/Petrov-Galerkin finite element method. The effect of various parameters (axis ratios (0.25, 0.5, 0.75, 1), vertical location of obstacles (0.38, 0.577, 0.769), Reynolds number (300, 500, 800, 1000)) on fluid flow and heat transfer characteristics in the channel with and without obstacles are compared and quantified. The recirculation region length of the double backward-facing stepped channel with obstacles decreases after the first and second steps when compared with no obstacles. The local Nusselt number distribution along the corner regions of the stepped wall is enhanced due to obstacles. The axis ratio of obstacles has less influence on the convective heat transfer enhancement than the vertical location of the obstacles.

Numerical study of the cavitating flow over backward facing step with a polydisperse two-phase flow model

We study the cavitating flow over a backward facing step with an incompressible polydisperse cavitation model. The model can predict experimental observations for this flow reasonably well, including the shedding cloud characterized by the condensation front, cavity length, void fraction, and shedding frequency. All model variations produced shedding cavities, but the turbulence model and grid resolution are essential for better predictions, with delayed detached eddy simulation (DDES) performing better than Reynolds-averaged Navier–Stokes. Quantities, such as pressures at key points, maximum void fraction location, and shedding frequency, are mildly sensitive to those factors. Finer DDES grid resolution, crucial to resolve small vortices where cavitation occurs in their low pressure cores, improves predictions. Since a fully incompressible model produces a condensation front that follows well the experimental trends, it is concluded that compressibility is not a necessary condition for the formation of a condensation front. Consequently, the speed of sound in the mixture does not appear to play an important role in the front formation and evolution. The polydisperse nature of the model allows prediction of the bubble size distribution. Small bubbles concentrate on the downstream section of the cavity, where cavity collapse is strongest and bubble fission is most intense, while larger bubbles reside near the step where the flow is milder. The condensation front is a moving source of vorticity for the liquid phase where the “compressibility,” in the sense of mixture density changes due to void fraction changes, and baroclinic effects are significant, but the buoyancy effect is negligible.

Effects of various backward-facing steps on flow characteristics and sediment behaviors

The study of flow over various steps behind the hydraulic structures, such as weirs, dams, spillways, barrages, and flood gates, is still of particular interest to researchers due to the complexity of flow characteristics and sediment behaviors at near-bed region. This study investigates the effect of various inclined backward-facing step (BFS) angles on near-bed turbulent flow structures and bedload transport rate in surface jet flow regime. A combined numerical technique of large eddy simulation and discrete element method, based on the open sources package OpenFOAM, is employed. The validation of the numerical model shows a good agreement between the simulation results and observed data obtained from different experiments. The simulation results reveal that the flow does not form a separation zone when the BFS angle is less than 20°, wherein the near-bed turbulence intensity is insufficient to induce substantial sediment movements. As the step angle is increased to a certain value (20°), the separation flow is formed. Consequently, the near-bed turbulence intensity is significantly increased due to the splat effect, and the sediment flux is also drastically increased. As the BFS angle further increases to 30° and 90°, the reattachment length is extended without notable changes in maximum turbulence intensity near the bed. The peaks of the mean bedload transport rate are located further downstream along the extended reattachment length. The quadrant analysis for bedload transport is performed to quantify the interactions between the flow and sediment movement. The results demonstrate that the sweep event plays significant role in moving most sediment to downstream of the reattachment point. On the other hand, right upstream of the reattachment point, the burst becomes the dominant turbulence event to move the majority of the sediment backward in the upstream direction.

Study of Heat Transfer and Flow Mechanism in Circular Backward-Facing Step Considering Ferrofluid Flow Under Magnetic Field Effect

Study of Heat Transfer and Flow Mechanism in Circular Backward-Facing Step Considering Ferrofluid Flow Under Magnetic Field Effect

Hybrid data assimilation methods, Part I: Numerical comparison between GEIM and PBDW

Hybrid Data Assimilation (HDA) methods are a class of numerical methods that aim at integrating Model Order Reduction (MOR) techniques into a Data Assimilation (DA) framework, thus combining mathematical models and experimental data. The objective is to reduce the solution time using MOR algorithms whilst keeping the accuracy of the models at the desired level using observations, which serve as an update to the a priori prediction of the model. This two-part work investigated HDA techniques by applying them to two classes of problems: numerical benchmark cases (part 1) and experimental facilities (part 2). In particular, this paper discusses the former, focusing on the numerical formulation of the methodologies and on the effect of noisy data. Indeed, real-world experimental data are always polluted by errors and uncertainties; therefore, it is critical to first assess the performance of these techniques on numerical benchmark cases with the artificial introduction of random noise before applying them to real-world experimental facilities. As such, this paper applies the Generalised Empirical Interpolation Method (GEIM) and the Parameterised-Background Data-Weak (PBDW) formulation to a non-adiabatic airflow over the classical computational fluid-dynamics benchmark of the 3D Backward Facing Step (BFS). Results show how both algorithms are valuable tools to reconstruct the state of the system when measurements are available, whilst assessing the effect of noise on the available data; in particular, the GEIM is a bit better than the PBDW since a lower reconstruction error is achieved with fewer sensors.

Hydrodynamic analysis of bioinspired vortical cross-step filtration by computational modelling.

Research on the suspension-feeding apparatus of fishes has led recently to the identification of novel filtration mechanisms involving vortices. Structures inside fish mouths form a series of 'backward-facing steps' by protruding medially into the mouth cavity. In paddlefish and basking shark mouths, porous gill rakers lie inside 'slots' between the protruding branchial arches. Vortical flows inside the slots of physical models have been shown to be important for the filtration process, but the complex flow patterns have not been visualised fully. Here we resolve the three-dimensional hydrodynamics by computational fluid dynamics simulation of a simplified mouth cavity including realistic flow dynamics at the porous layer. We developed and validated a modelling protocol in ANSYS Fluent software that combines a porous media model and permeability direction vector mapping. We found that vortex shape and confinement to the medial side of the gill rakers result from flow resistance by the porous gill raker surfaces. Anteriorly directed vortical flow shears the porous layer in the centre of slots. Flow patterns also indicate that slot entrances should remain unblocked, except for the posterior-most slot. This new modelling approach will enable future design exploration of fish-inspired filters.

Wind tunnel test of airfoil with erosion and leading edge protection

This paper describes wind tunnel tests of a NACA 633 – 418 airfoil with erosion and leading edge protection. Measurements are carried out at high Reynolds number (Re = 5 million) representing modern wind turbines. Three examples of deviations from the perfect airfoil surface are shown. It is seen how the presence of a roughness mesh degrades the aerodynamics and that the presence of the mesh is more important than the actual topology of the mesh. That is also the case for the stall strips where a small strip influences the performance slightly less than a big stall strip, but the presence of the stall strip alone is influencing the performance significantly. Finally, a simulated leading edge protection (LEP), represented by a sheet of paper, can influence the performance significantly as the paper leads to a backward facing step. Furthermore, the measurements showed that correct mounting of LEP is important to avoid too big losses in aerodynamic performance. Investigating the impact of reduced airfoil performance for the rotor performance showed losses in annual energy production of between 0.3% and 4.0%. All in all the wind tunnel tests reflected that leading edge damages have a significant impact on the aerodynamic performance.

Numerical Investigation by Cut-Cell Approach for Turbulent Flow through an Expanded Wall Channel

The expanded wall channel backward-facing step (BFS) and axisymmetric diffuser plays an important role in the society of fluid dynamics. Using a cut-cell technique is an established new method to treat the inclined wall of an axisymmetric diffuser. Cut-cell handle to reach the shape of the inclined wall, an axisymmetric diffuser and complex geometry. It helps treat the boundary condition at the wall in an accurate physical way. The turbulent flow through the geometries is solved by using Reynolds averaged Navier-Stokes equations (RANS) with the standard k-ε model. A self-built FOTRAN code based on the finite volume method with the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm for pressure velocity coupling is established and examined with published experimental data for two different geometries backward-facing step (BFS) and axisymmetric diffuser. The results of the new technique reflect good agreement between the numerical results and the experimental data. A parametric study of the impact of area ratios (2, 2.5, 3, 3.5) in a backward-facing step on pressure, velocity, and turbulent kinetic energy. The angles (7°, 10°, 14°) and area ratios (2, 2.5, 3, 3.5) effect of an axisymmetric diffuser on the streamlines, local skin friction, pressure, velocity, turbulent kinetic energy, and separation zone.

Data-driven wall modeling for turbulent separated flows

The large-eddy simulation of wall-bounded turbulent flows at high Reynolds numbers is made more efficient by the use of wall models that predict the wall shear stress, allowing coarser cell sizes at the wall. In this paper, a data-driven approach for the modeling of the wall shear stress is examined using filtered high-fidelity numerical data from two fully developed turbulent channel flows and two turbulent flows with separated regions: a three-dimensional diffuser and a backward-facing step. The model is a multilayer perceptron based on the flow information in the vicinity, given by the distance to the wall and the velocity components at a given number of grid points above the wall. The model is Mach number equivariant at the quasi-incompressible limit, Galilean invariant, statistically rotational invariant and can extrapolate to flow conditions unseen in the training dataset. The relevance of the machine-learning procedure is verified a priori using the filtered numerical data and a posteriori by performing wall-modeled large-eddy simulations implementing the model. The results show that the model is able to leverage the local spatial information to discriminate developed wall turbulence and separated regions in flow configurations not included in the training dataset.

Numerical and Experimental Analysis of the Cold Flow Physics of a Nonpremixed Industrial Gas Burner

Abstract The flow field of a nonpremixed industrial gas burner is analyzed with Reynolds-averaged Navier–Stokes computational fluid dynamics validated against velocity and pressure measurements. Combustion is not modeled because the aim is optimizing the predictive capabilities of the cold flow before including chemistry. The system's complex flow physics, affected by a 90 deg turn, backward and forward facing steps, and transversal jets in the mainstream is investigated at full and partial load. The sensitivity of the computed flow field to inflow boundary condition setup, approach for resolving/modeling wall-bounded flows, and turbulence closure is assessed. In the first sensitivity analysis, the inflow boundary condition is prescribed using measured total pressure or measured velocity field. In the second, boundary layers are resolved down to the wall or modeled with wall functions. In the third sensitivity analysis, the turbulence closure uses the k−ω shear stress transport eddy viscosity model or two variants of the Reynolds stress model. The agreement between the predictions of most simulation setups among themselves and with the measurements is good. For a given type of inflow condition and wall flow treatment, the ω-based Reynolds stress model gives the best agreement with measurements among the considered turbulence models at full load. At partial load, the comparison with measured data highlights some scatter in the predictions of different patterns of the flow measurements. Overall, the findings of this study provide insight into the fluid dynamics of industrial gas burners and guidelines for their simulation-based analysis.

Mixing and combustion characteristics in a scramjet combustor with different distances between cavity and backward-facing step

The mixing and combustion characteristics in a cavity flameholding combustor under inlet Mach number 2.92 are numerically investigated with ethylene injection. Dimensionless distance is defined as the ratio of the actual distance to the height of the combustor entrance. The cavity shear-layer mode, the lifted cavity shear-layer mode, and jet wake mode with upstream separation are observed respectively with dimensionless distance equals to 1.5, 4.5, and 7.5. In both non-reacting and reacting flow fields, the numerical results are essentially in agreement with the schlieren photography, flame chemiluminescence images, and wall pressure, which verify the reliability of the numerical method. The results of non-reacting flow fields show that the Backward-Facing Step (BFS) can promote the flow separation downstream at a fixed distance. The more forward the separation position is, the larger the separation zone is in the non-reacting flow field. Furthermore, the larger the separation zone is, the higher the intensity of combustion in the reacting flow field is. A reasonable distance can reduce the total pressure loss generated by the shock waves in the combustor. The flame presents remarkable three-dimensional characteristics in the reacting flow fields. When dimensionless distance equals to 4.5, there are flames near the side wall above the cavity and it is difficult for the flame stabilization in the center of the combustor, while the combustion intensity in the center of the combustor is higher than that near the side wall when dimensionless distance equals to 7.5. In the cavity flameholding combustors with a backward-facing step, the higher combustion intensity may bring much total pressure loss to the combustor. Thus, it is a good choice to achieve better thrust performance when dimensionless distance equals to 4.5 compared to the other two combustors.

A Simple Criterion for Estimating the Grid Level of Detail for RANS Methods

A simple criterion for evaluating the grid resolution needed to obtain a grid-independent solution of turbulent flow problems in the framework of statistical approach to turbulence simulation is proposed. The criterion is derived on the basis of an a posteriori estimate of the local interpolation error of the field of turbulent kinetic energy. A good resolution should ensure a small local interpolation error of the discrete turbulent kinetic energy. The equation for the transport of turbulent kinetic energy and realizability conditions for the turbulent stress tensor made it possible to reduce the estimation of relative interpolation error to an explicit formula for the estimate of the maximal grid step required for obtaining a grid-independent solution. The proposed criterion is applied to a steady problem for a flow past a backward facing step and to the problem of unsteady flow around a half-circular profile arranged at a zero angle of attack for the Reynolds number Re = 45 000. A numerical study showed that the proposed criterion gives a good estimate of the grid resolution required for obtaining a grid-independent solution away from a wall. This criterion can be used both for estimating the grid independence of the solution and for adapting the computation grid.

Flame Dynamics in an Optically Accessible Solid Fuel Ramjet Combustor

Flow–flame interactions were investigated in an optically accessible solid fuel ramjet combustor. Experiments were performed with a single hydroxyl-terminated polybutadiene fuel slab located downstream of a backward-facing step in a rectangular chamber. To emulate flight-relevant combustor conditions, unvitiated heated air was directed through the combustion chamber with an inlet temperature of , chamber pressures of 450–690 kPa, and port Reynolds number of . To characterize the heat-release distribution and velocity field, 20 kHz -chemiluminescence and 10 kHz particle imaging velocimetry measurements were used. Comparison between the mean chemiluminescence images acquired at three flow conditions indicates reduction in flame height above the grain with increasing air mass flow rate. Dominant heat-release coherent structures in the statistically stationary flow are identified using the spectral proper orthogonal decomposition technique implemented on time series of instantaneous images. The spatial mode shapes of the chemiluminescence and velocity field measurements indicated that the flow–flame interactions were dominated by vortex shedding generated at the backward-facing step in the combustor, at Strouhal numbers of 0.06–0.10. The frequency corresponding to these modes is shown to be invariant of air mass flux, indicating that system dynamics are primarily dependent on the backward-facing step geometry and the bulk velocity in the combustor.

Effect of the Curvature Angle in a Conduit with an Adiabatic Cylinder over a Backward Facing Step on the Magnetohydrodynamic Behaviour in the Presence of a Nanofluid

A backward facing duct are present in various industrial applications especially those focused on heat transfer. The flow through a curved backward facing duct especially in the presence of nanofluid presents complexities compared to a straight backward facing step (BFS) duct. Therefore, the present numerical study deals a nanofluid flow (Fe3O4-H2O) forced convection in a curved backward facing duct. The objective of this investigation is to visualize at different curvature angles g (0°, 30°, 45°, 60°, 90°) imposed on the top wall of the duct, the effect of Hartmann number Ha (0, 50, 100), magnetic field inclination angle γ (0°, 60°, 90°), Reynolds number Re (10, 100, 200) and nanoparticle volume fraction φ (0 %, 0.05 %, 0.1 %). The dimensionless governing equations are solved using the multigrid finite element method. The results showed that the heat transfer was enhanced at the curved angle g = 90° for large Hartman numbers, thus, the average Nusselt number increased with a ratio of 240.74 % in the case of Hartmann number (Ha = 100).

Influences of steps in hybrid rocket engines:Simulation and validation on simplified geometries

In this study, we investigate the effect of single steps inside the fuel grains of typical hybrid rocket motors numerically. Steps can be a promising candidate to increase the regression rate of hybrid engines. We show that simulations on simplified geometries yield surprisingly close numerical regression rate profiles when compared to experimental data. Moreover, there is no necessity to calculate the progression of the fuel port at different time steps, as a single simulation on the average diameter can match the experiments sufficiently well. This observation allows for larger parametric studies on optimal positioning of the steps while limiting computational resources. The potential to increase the average regression rate through steps can be predicted numerically, and the simulations are following the same trend as the experiments. The augmented mixing and heat transfer inside the turbulent boundary layer can be predicted. It is concluded that backward facing steps increase the regression rate proportional to the step height up to 10 mm, and are preferably utilized upstream. For forward facing steps, the regression rate augmentation is saturated starting with 5 mm step height, and the position should be further downstream.

Measurements on the effect of steps on the transition of laminar boundary layers

The effects of steps on the transition of laminar boundary layers were measured on a flat plate for low Reynolds numbers with critical and subcritical step heights. The transition position was measured by determining the intermittency distribution in streamwise direction, including the characteristic length of the transitional region. The results are compared with formulations of a critical step Reynolds number {textrm{Re}_textrm{h}}, i.e., the step height that will instantly trigger transition at the step position, and—for subcritical step heights—with {{Delta N}}-formulations from the literature. For backward-facing steps, the concept of a step Reynolds number can be used to distinguish between subcritical and critical step heights, whereas for forward-facing steps there seems not to be one unique {textrm{Re}_textrm{h}}. Furthermore, for subcritical backward-facing steps the concept of a {{Delta N}}-approximation gives a reasonable description of the experimental observations. Again in contrast, for forward-facing steps a {{Delta N}}-approach scattered a lot and no clear dependency was found between the reduction in the critical N-factor of transition and the relative step height.