Forward-facing Step Research Articles

A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations

The main result in this paper is a provably entropy stable shock capturing approach for the high order entropy stable Discontinuous Galerkin Spectral Element Method (DGSEM) based on a hybrid blending with a subcell low order variant. Since it is possible to rewrite a high order summation-by-parts (SBP) operator into an equivalent conservative finite volume form, we were able to design a low order scheme directly with the Legendre-Gauss-Lobatto (LGL) nodes that is compatible to the discrete entropy analysis used for the proof of the entropy stable DGSEM. Furthermore, we present a hybrid low order/high order discretisation where it is possible to seamlessly blend between the two approaches, while still being provably entropy stable. With tensor products and careful design of the low order scheme on curved elements, we are able to extend the approach to three spatial dimensions on unstructured curvilinear hexahedral meshes. We validate our theoretical findings and demonstrate convergence order for smooth problems, conservation of the primary quantities and discrete entropy stability for an arbitrary blending on curvilinear grids. In practical simulations, we connect the blending factor to a local troubled element indicator that provides the control of the amount of low order dissipation injected into the high order scheme. We modified an existing shock indicator, which is based on the modal polynomial representation, to our provably stable hybrid scheme. The aim is to reduce the impact of the parameters as good as possible. We describe our indicator in detail and demonstrate its robustness in combination with the hybrid scheme, as it is possible to compute all the different test cases without changing the indicator. The test cases include e.g. the double Mach reflection setup, forward and backward facing steps with shock Mach numbers up to 100. The proposed approach is relatively straight forward to implement in an existing entropy stable DGSEM code as only modifications local to an element are necessary.

Influence of a Forward-Facing Step Surface Irregularity on Swept Wing Transition

An experimental study has been carried out to determine the influence of a forward facing-step (FFS) on the laminar–turbulent transition of a swept wing boundary layer. Wind tunnel experiments were conducted at a fixed 3 deg angle of attack and varying Reynolds number between 2.5 and 4.5 million. Moreover, the FFS influence was investigated under unforced (i.e., smooth leading edge) and forced conditions (i.e., using discrete roughness elements). For each test case infrared thermography was used to determine the transition location and spatial organization of the crossflow vortices. In addition, the change in amplification factor was calculated using linear stability theory. Results reveal the importance of considering multiple parameters when estimating the critical FFS height. The unforced cases indicate that one-parameter correlations (i.e., based on the crossflow vortex core height or boundary-layer displacement thickness) might not be sufficient to universally capture the dynamics of these complex flows. Analysis of the forced cases shows that in addition to local parameters (i.e., step height and vortex core height), the FFS influence on transition depends on the stability characteristics of the incoming instability mode. These findings suggest a complex nonlinear interaction between instabilities and surface irregularities, which highlight the need for multiparameter correlations for accurate transition prediction.

Boundary Layer Transition Preflight Experiments in a Mach-6 Quiet Tunnel

Experiments on a subscale model of the U.S. Air Force Office of Scientific Research Boundary Layer Transition flight experiment were made in the Boeing/Air Force Office of Scientific Research Mach-6 Quiet Tunnel. Infrared thermography and temperature-sensitive paint were used to measure the surface temperature and heat transfer and provide images of streamwise streaks with the model at 0, 2, and 4 deg angle of attack. Variations in heating patterns were measured for yaw and roll angles. All smooth body cases remained laminar under quiet flow, but symmetric turbulent wedges were seen in noisy flow. Discrete surface pressure sensors measured possible instabilities on the model surface at locations that correspond to computed instability growth. It was discovered that the geometry was sensitive to forward- and rearward-facing steps near the swept leading edges. Controlled forward- and rearward-facing steps were created and tested. No transition was measured under quiet flow for any rearward-facing step at 0 deg angle of attack. Early transition was measured for the forward-facing steps, and correlations were developed for scaling step effects to the flight vehicle.

Influences of Steps on the Hypersonic Boundary-Layer Transition on a Cone

The influences of steps on the hypersonic boundary-layer transition on a cone are investigated in a hypersonic quiet wind tunnel, using high-frequency pressure sensors and nano-tracer-based planar laser scattering (NPLS) techniques. The high-frequency surface pressure fluctuations are analyzed using power spectral density analysis, band-pass filtering, and cross-correlation calculation. Quantitative analysis of the NPLS images is carried out based on the grayscale information and time interval. The results demonstrate that the second-mode wave amplitude increases initially and then drops along the streamwise, whereas the characteristic frequency decreases monotonously. However, the second-mode wave amplitude in the 0.4 mm () and 0.6 mm () forward-facing step models is constantly rising, and the obvious second-mode wave first appears closer to the downstream than the smooth cone, which suggests that the forward-facing steps could suppress the second-mode disturbances and shifts the transition downstream. Nonetheless, there is only a clear promotion effect when the height of the forward-facing step is 1.6 mm (). In addition, the backward-facing step could destabilize the boundary layer and shift the transition upstream, and this effect is enhanced by increasing the step height.

Simulation of Convective Heat Transfer in 3D Forward Facing Step Using Various Turbulence Models

In this work, a modified solver from the OpenFOAM 4.1 software was used to study the fluid flow and heat transfer characteristics over a forward facing step (FFS) considering various turbulence models, viz., k-e , k-ω , k-ω SST and v 2 -f . Numerical computations were performed using a newly developed transient solver, pisoTempFoam. Modeling and meshing of the geometry and setting of the boundary conditions were done with OpenFOAM. The bottom (upstream, step and downstream) walls were heated at a constant temperature of 350K, while the fluid inlet temperature was 298K. The simulation results were compared with those available in the literature. Variation of skin friction coefficient ( C f ), coefficient of pressure ( C p ), and Nusselt number (Nu) for different Reynolds numbers (Re), contraction ratios (CR) and different fluids are presented. This article also presents information about recirculation bubbles in the upstream and downstream regions of the FFS. The results show that the combined effect of turbulence models and parameters, such as CR, Re and Pr, change the flow and heat transfer characteristics of the FFS. The present CFD simulation plays a pivotal role in the analysis of flow over airfoils at a large angle of attack in heat exchangers and pipes whose area suddenly changes.

On the use of the pressure jump approach for the simulation of separated external flows around porous structures:A forward facing step

The evaluation of the aerodynamic behaviour of porous structures currently represents a problem of growing interest for the Wind Engineering community. However, due to the presence of pores, the measurement of pressures around such structures is not easily accomplished by means of standard experimental procedures. Computational Fluid Dynamics might provide a detailed characterization of the flow, but prohibitive computational costs are required to explicitly simulate the body geometry taking the pores into account. A convenient alternative is to use appositely defined pressure jumps which account for the presence of the porous surface, without simulating its details. In this contribution, a new relation which links the pressure jump to the surface porosity is proposed. Then the flow over a forward facing step, composed by a vertical porous surface and a horizontal solid surface, is simulated by means of Large Eddy Simulations. Results show that, despite different internal arrangements of the separation bubble are predicted, results obtained with different modelling approaches are in reasonable agreement with each other.

Three-dimensional wind-turbine wake characterization via tomographic particle-image velocimetry

Wind turbines are often sited on different topographical features. In the current work, we performed wind-tunnel measurements of the wake behind a single wind turbine sited on two escarpments differing in the windward side shape using tomographic particle-image velocimetry. The escarpments are classified as forward facing step (FFS) and ramp-shape. The turbine sited on the FFS experiences an inflow with high flow shear and turbulence due to flow separation from the escarpment leading edge compared to the one on the ramp-shaped escarpment. As a consequence, the wake characteristics behind the turbine are strongly affected by the shape of the topography. The velocity deficit in the wake of the turbine is relatively higher in the forward facing step shape, but it also shows a faster recovery. The rotation of the wake is stronger for the turbine on the ramp-shaped escarpment, whereas the meandering of the wake is higher for the FFS case. The spatial coherence is observed to be higher in the near wake of the turbine sited on the FFS escarpment, while it is very similar in the far wake for both cases. Instantaneous vortices identified by the Q-criterion show that the development of tip and hub vortices is affected by the topography as well.

DSMC investigation of rarefied gas flow over a 2D forward-facing step: Effect of Knudsen number

A Forward-Facing Step (FFS) can be approximated as a simplified geometry for modeling the irregularities around space vehicles, the flow around which is often rarefied. These irregularities lead to flow separation, circulation, and re-attachment. This study aims to examine one of the fundamental surface irregularities that can have a significant effect on the design of space vehicles. In this article, Direct Simulation Monte Carlo (DSMC), an effective method for studying rarefied flows, is used to investigate the role of rarefaction on the non-reacting hypersonic rarefied gas flow over a forward-facing step. A comprehensive analysis of the effects of Knudsen number on the on flow-field properties, i.e., velocity, pressure, temperature, density, and surface properties, i.e., pressure coefficient, skin friction coefficient, and heat transfer coefficient is performed. The selected Knudsen number range from 0.05 to 21.33, covering the various rarefaction regimes. The Mach number of the free-stream flow employed was 25. The sections in the vicinity and downstream of the step are examined in-depth, describing the predominant nonequilibrium aspects. The normalized flow properties increased with Knudsen number and are primarily affected by the interplay of compressibility and viscous dissipation effects. Flow recirculation occurred in the slip and transition regime, whereas it was absent in the free-molecular regime; moreover, the recirculation lengths decreased with rarefaction. The surface properties were found to increase with Knudsen number with peak magnitudes located on the upstream and frontal face of the step.

Sound radiated by turbulent flow over unrounded and rounded forward-facing steps

This study presents measurements of the far-field noise radiated by forward-facing steps with and without rounded corners. A noise prediction formula, obtained by combining theory and measurements, to predict noise radiated by an unrounded forward step is also presented. The prediction methodology has also been extended to include the effects of rounding the step corner. The height of the step in measurements ranged between 78% to 84% of the incoming, turbulent wall-jet boundary layer. The Reynolds number based on step height was between 8300 and 16,800. Six roundings of the step corner were considered with radii equal to 0%, 6.25%, 12.5%, 25%, 50%, and 100% of the step height. It was found that rounding the forward step corner reduces the noise without affecting its directivity and scaling significantly. A slight rounding of the corner only affects the noise at high frequencies, however, a further increase in rounding leads to a broadband noise reduction. The prediction formula for the unrounded forward step yields reasonably good agreement with both past and present measurements. The predictions also suggest that the noise generated by a forward step is independent of the incoming boundary-layer thickness and scales with the step height. The predictions for rounded forward steps show that the noise attenuation due to corner rounding can be reasonably approximated if it is assumed that the unsteady surface loading in the vicinity of rounded steps scales with the reattachment length associated with each rounding.

Heat transfer and flow structure through a backward and forward-facing step micro-channels equipped with obstacles

This study presents 2-D simulations of a flow-through a sudden expansion/contraction micro-channel with the existence of obstacles. The bottom wall is maintained at constant flux, while the other walls are adiabatic. Rectangular adiabatic obstacles are mounted before the expansion region on the upper and lower wall of the channel used. The finite element method was used to discretize the equations that govern the physical model. Results indicate the apparition of a separate vortex, situated in the corner after the sudden expansion of the micro-channel for low Reynolds numbers. For higher values and expansion ratios, the vortex separation length increases. The obtained results show that the obstacles have a considerable effect on the dynamics of the flow and enhancement of heat transfer.

Drag increment induced by a small-scale forward-facing step in Mach number 5 turbulent boundary layer flows

Small-scale roughness elements or imperfections are inevitable over the surface of a flight vehicle. The aerodynamics of these small-scale structures is difficult to predict but may play an important role in the design of a flight vehicle at high speed. The forward-facing step is a typical type of roughness element. Many experiments have been conducted to study the aerodynamics of supersonic forward-facing step, especially with a step height larger than boundary layer thickness. However, few studies focus on small steps. To improve the understanding of small-scale forward-facing step flow, we perform a series of simulations to analyze its aerodynamic influence on a Mach number 5 turbulent boundary layer. The general flow structures are analyzed and discussed. Several shock waves can be induced by the step even if the step height is much smaller than the boundary layer thickness. Two significant shocks are the separation shock and the reattachment shock. The influenced area by the step is limited. With the increase of the step height, the non-dimensional influence area decreases and gradually converges when the step height reaches the boundary layer thickness. There are two normalized distributions of the skin friction coefficient and pressure coefficient associated with step height. By using the normalized parameters, a power-law relationship between the step height and the drag increment coefficient is revealed and fits the simulation results well. It is further illustrated that this relationship still holds when changing the inlet angle of attack, but needs slight modification with the angle of attack.

Mechanisms of stationary cross-flow instability growth and breakdown induced by forward-facing steps

Mechanisms of stationary cross-flow instability growth and breakdown induced by forward-facing steps

Effect of suction on laminar-flow control in subsonic boundary layers with forward-/backward-facing steps

In a subsonic boundary layer, a forward-facing step (FFS) or a backward-facing step (BFS) usually destabilizes the oncoming Tollmien–Schlichting (T-S) waves, leading to a promotion of laminar–turbulent transition. This paper studies a laminar-flow control strategy by introducing wall suction immediately ahead of the FFS or behind the BFS. The impact of the step–suction combination on an oncoming T-S wave is quantified by a transmission coefficient, defined as the ratio of the asymptotic amplitude downstream of the step and suction to that upstream. In order to solve this problem, a local scattering theory based on the large-Reynolds number (large-R) asymptotic framework and a Harmonic linearized Navier–Stokes approach, that calculates the perturbation field at finite Reynolds numbers, are employed. The latter approach is confirmed to be accurate by comparing its results with direct numerical simulations, and the results given by the two approaches agree when the Reynolds number is asymptotically large. According to the large-R triple-deck formulism, a few control parameters, such as the Mach number, Reynolds number, and wall temperature, disappear, which makes a systematical parametric study possible. The destabilizing effect of a step increases with its height, while the stabilizing effect of suction increases with its flux. For a step with a moderate height, suction with a small flux is sufficient to compensate the destabilizing effect of the step.

Spatio-temporal dynamics of flow separation induced by a forward-facing step submerged in a thick turbulent boundary layer

The effects of large-scale motion (LSM) on the spatio-temporal dynamics of separated shear layers induced by a forward-facing step submerged in a thick turbulent boundary layer (TBL) are investigated using a time-resolved particle image velocimetry. The Reynolds number based on the free-stream velocity and step height was 13 200. The oncoming TBL was developed over a cube-roughened surface and the thickness was 6.5 times the step height. The step height was chosen to coincide with the elevation where the dominant frequency of streamwise fluctuating velocity in the TBL occurred. At this elevation, the local turbulence intensity was 14.5 %. Distinct regions of elevated Reynolds stresses were observed upstream and downstream of the leading edge of the step. The unsteady dynamics of the separation bubbles upstream and downstream of the step was investigated using the reverse flow area. Both separation bubbles exhibit low-frequency flapping motion, and the dominant frequency of the downstream separation bubble is identical to the dominant frequency of the streamwise fluctuating velocity in the oncoming TBL at the step height. As the low-velocity region of LSM passes over the step, the downstream separation bubble is enlarged and subsequently undergoes a high-frequency oscillation. Turbulence motions were partitioned into low-, medium- and high-frequency regimes based on spectral analysis of the Reynolds stresses. The contributions from these partitioned turbulence motions are used to elucidate the effects of LSM on the elevated Reynolds stresses in the shear layers upstream and downstream of the step.

An adaptive mesh refinement approach based on optimal sparse sensing

We introduce a new approach for adaptive mesh refinement in which adaptivity is driven by low rank decomposition and optimal sensing of the dynamically evolving flow field. This method seeks an ordered set of locations for mesh adaptation from the instantaneous data-driven basis of an online proper orthogonal decomposition of the velocity, which organizes features into sparse optimal orthogonal modes based on an energy norm. The sensing is achieved via a computationally expedient discrete empirical interpolation method using rank-revealing QR factorization (Drmac and Gugercin SIAM J Sci Comput 38(2):A631–A648, 2016). The methodology is applicable to a wide range of numerical discretizations, and is tested on a spatiotemporally evolving incompressible turbulent jet, a complex wind turbine wake, and supersonic flow over a forward-facing step. The proposed approach is demonstrated to predict accurate velocity statistics and yield significantly smaller grids in comparison to gradient-based methods. The algorithm is seen to focus refinement in the vicinity of dynamically significant regions such as those characterized by high turbulence kinetic energy, coherent structures and shock interactions. Moreover, the approach does not require parameters or thresholds, which may be difficult to obtain for complex flows, to be known a priori to facilitate mesh adaptation.

Surface Step Effects on Boundary-Layer Transition Dominated by Tollmien–Schlichting Instability

Surface step effects on boundary-layer transition are modeled using a variable -factor method for transition dominated by Tollmien–Schlichting instabilities. Experimental correlations provide a bounding expression for the change in the critical -factor for transition onset, which provides a predictive means to account for surface steps. An investigation is conducted to assess the applicability of this approach for more general step arrangements. The approach is applied to capturing the superposition of a forward-facing and a backward-facing step in the form of a rectangular protrusion or a wide gap. Results show that a rectangular protrusion is well modeled by a linear combination of steps. However, a wide gap is best represented by a backward-facing step, without regard for the following forward-facing step. The sensitivity to streamwise step position is also investigated. Results show that the method is effective at capturing step effects for step positions in the neighborhood of the instability neutral point, and extending downstream close to the smooth-surface transition location. The effects of steps placed well upstream of the instability neutral point are overpredicted by the step model, likely the result of nonparallel effects on the upstream decay or as a result of the underlying receptivity occurring in the neighborhood of the neutral point.

Analysis of turbulent flow in a channel roughened by two-dimensional ribs: effect of first rib width

This work investigates the turbulent flow in a channel roughened by seven ribs of rectangular cross section disposed transversely. The flow configurations of identical ribs from the first one generate a large eddy spreading along the top of the two first ribs, trapping the flow of the first cavity. The widening of the first rib may solve this problem. Therefore, this flow configuration might be required in building structure applications necessitating regular structures from the first cavity. Streamlines contours indicates that the first rib behaves as a forward facing step when L1 > 5h (L1 is the first rib width), regular structures of the flow occurs from the first cavity. The effect of wider first rib is highlighted by friction and pressure coefficients profiles and those of the turbulent kinetic energy. Its effect also appears in the Darcy friction factor. The viscous and pressure forces applied on the first rib and the 5th pitch roughness indicate that the pressure force is dominant. Darcy friction factor characterizing the flow and pressure drag coefficient evaluated at the 5th pitch roughness remains independent of Reynolds number, while the drag force applied on the first rib increases when Reynolds number augments.

Development of a data-driven model for turbulent heat transfer in turbomachinery

Machine Learning (ML) algorithms have become popular in many fields, including applications related to turbomachinery and heat transfer. The key properties of ML are the capability to partially tackle the problem of slowing down of Moore’s law and to dig-out correlations within large datasets like those available on turbomachinery. Data come from experiments and simulations with different degree of accuracy, according to the test-rig or the CFD approach. When dealing with modelling of turbulent flows in turbomachinery there is a constant trade-off between accuracy and computational costs, but starting from the large amount of data on turbomachinery performance, with ML it is possible to train a learner to correct and improve CFD. The aim of this work is to investigate an innovative data-driven approach that could lead to a significant improvement in the analysis of heat transfer in turbulent flows. The effects of Reynolds number and wall temperature on heat transfer for a double forward-facing step with two squared obstacles were investigated by numerical simulations carried out in OpenFOAM. Then a machine-learnt model was derived using a regression algorithm. The results of regressor showed that a data-driven approach can effectively predict results of the RANS model.

A comparative analysis of flow features of Newtonian and power law material: A New configuration

In recent years, material analysis of fluids has generated prodigious interest of researchers due to their effective role in interdisciplinary sciences. In view of its importance, the present communication is devoted to analyze the flow of power law fluid representing the features of shear thinning, shear thickening and Newtonian materials. Constitutive equations expressed in the form of tensorial representations depicting power law relation between viscosity and shear rate. The whole mathematical model is solved computationally via of finite element method by using stable P2−P1 finite element pair. A highly refined hybrid mesh is obliged for the accurate computation of results. Material properties of power law fluid are disclosed in physical configuration renowned as channel driven cavity combining various benchmark problems like cavity flow, forward and backward facing steps and channel flow. Impact of material parameters on pertinent profiles is disclosed through graphs. Verification of computed results is done by comparing the velocity, viscosity, pressure fields for power law fluid with the Newtonian case.

CFD flow dynamics over model scarps and slopes

ABSTRACT Knowledge of wind flow over dune scarps and, as scarps fill, their subsequent various slopes, is important for understanding sediment transport pathways from beach to dunes. In this study, flow over scarps (also termed forward-facing steps) is reviewed, and the flow over a vertical scarp (90°) and three slopes of 45°, 24°, and 14°, all 2 m in height, is examined via CFD modelling. The flow over three 90° scarps, with heights of 1 m, 2 m and 4 m, and over a 2-m high vertical (90°) scarp for three oblique incident winds is studied. The extent of wind flow deceleration and separation becomes smaller with decreased slope, with maximum flow separation and reverse vortex development occurring on the vertical scarp. The extent of crest wind flow separation is greatest for the scarp and considerably less for the 45° slope. As scarp height increases, so too does the spatial extent of turbulent wind flow, wind speed, and extent of the flow separation region. As incident wind direction became more oblique over a vertical scarp, less deceleration occurs, and helicoidal vortices replace roller vortices. Our results demonstrate how scarp morphology and wind direction are likely to influence transport pathways.