Turbulent Separated Flow Research Articles

Anomalous intensification of vortex heat transfer in the case of separated air flow over an inclined groove in a hot isothermal region of a flat plate

Anomalous heat transfer intensification in turbulent separated air flow over a long groove of moderate depth made in a plate inclined at an angle of 45°to the freestream is revealed both experimentally and numerically. The region under investigation includes a rectangle heated to 100°C by saturated water vapor. The Reynolds number varied from 103to 3×104. Using the gradient heatmetry the twofold increase, as compared with the case of a flat plate, of the heat transfer coefficient on the groove bottom is established at the Reynolds number Re = 3×104. The relative Nusselt number in different regions of the groove is determined both in the physical experiment and in the RANS calculations with the application of multiblock computational technologies and the SST model in the VP2/3 software package. The results are in good agreement in the turbulent flow regime at Re = (5, 10, and 30) ×103.

On the spatio-temporal dynamics of cavitating turbulent shear flow over a microscale backward-facing step: A numerical study

The influence of cavitation on the mean characteristics and unsteady behavior of turbulent separated flows was comprehensively investigated in this study over a microscale backward-facing configuration at the Reynolds number (ReD) of 7440. The computational approach took both compressibility and finite mass transfer (Thermodynamic non-equilibrium) into account, to accurately capture the effects of shock waves, as well as to capture baroclinic phenomena on vortex dynamics within the turbulent separated flow. The compressibility effects were handled by using appropriate equation of states for each phase and for the mixture. Phase-change was considered through a transport equation for the vapor volume fraction, allowing for finite mass transfer contributions. Additionally, a wall adaptive large eddy simulation (LES) approach was utilized for simulating turbulent structures and their effects. The findings reveal that vapor development diminishes the mean growth rate of the shear layer and delays its reattachment to a longer distance from the step. Moreover, analysis of Reynolds normal and shear stresses, as well as the root mean square (RMS) of pressure fluctuations, demonstrates that the formation and collapse of vapor packets significantly influence turbulence decay and production in the second half of the shear layer and reattachment. It was also observed that both mean pressure and pressure fluctuations increased in vicinity of the reattachment region when cavitation was present, which was attributed to the condensation and collapse events. Spectral analysis further indicates the emergence of two dominant low frequency modes, linked to the displacement of the reattachment point. In the presence of cavitation, the frequencies associated with dominant Power Spectral Densities (PSDs) were smaller than those in the absence of cavitation. Additionally, each of these low frequencies corresponded to a specific vapor transport mechanism within the Turbulent Separation Bubble (TSB). Furthermore, it is shown that cavitation leads to a significantly higher spectral energy of high frequency fluctuations within the reattachment region in comparison to the condition where cavitation is absent. This can be attributed to the frequent collapse of bubbles in this region. At the end, we employed Spectral Proper Orthogonal Decomposition (SPOD) for modal analysis. This method offers valuable insights into the coherent structures and associated frequencies that arise in both the presence and absence of cavitation, which provides a deeper understanding of the effect of cavitation on the coherent structures and their dynamics.

RANS representation of transition and separation over a low-Re number blade section at high angle of attack

Systems based on wind energy harvesting can successfully meet part of the increasing green energy demand worldwide. However, wind turbines operation might be undermined by varying atmospheric conditions, which could result in an increase of angle of attack and consequent onset of flow separation phenomena, especially at low Reynolds numbers. Such conditions are strongly influenced by blades geometry, and they negatively affect structural integrity and power output of wind turbines. For this reason, it is crucial to define a tool capable of swiftly allowing numerical investigations on different geometrical configurations to delay and mitigate flow separation occurrence. The present work aims at modelling laminar-turbulent transition and turbulent flow separation over a wind turbine blade section operating at angle of attack = 15°, Re = 66000 and Pr = 0.71 by means of a steady RANS approach. Turbulence is treated by means of the Transition SST k-ω and the Transition k-kL-ω models. The main aerodynamic and thermal coefficients are evaluated and compared against a high-order accurate DNS database for validation. The results highlight, for the present test case, a better capability of the Transition SST k-ω of perceiving the main thermo-fluid dynamic features of the separated flow over the blade section.

Regulating turbulent separation by surface microstructures on a blunt plate

Microstructured surfaces can induce secondary flow and regulate flow structures of the turbulent separation flow. However, the mechanism governing the relationship between the microstructure size and the characteristic flow size remains unclear. In this study, the separated flow over a blunt flat plate with surface microstructures is studied using time-resolved particle image velocimetry experiments and implicit large-eddy simulations for the plate-thickness-based Reynolds number from 5.08×103 to 1.31×104. The ratio of the height of microstructures to the plate thickness (h/d) ranges from 0.01 to 0.1. Combining experimental and numerical results, the relationships between the separation bubble size and the microstructure size under different Reynolds numbers exhibit similarity when normalized by the separation bubble size of the smooth plate. The dimensionless separation bubble size decreases when the microstructure height increases and large microstructures (h/d = 0.1) exhibit good performance on reducing the flow separation. Near the leading edge, the distortion of two-dimensional vortices and the generation of three-dimensional hairpin vortices are promoted by the first several rows of large microstructures. Additionally, in the main separation region, secondary positive spanwise vortices emerge from large microstructures. Subsequently, the secondary vortices lift up and evolve into streamwise vortices. The characteristic scale of secondary vortices is represented by a significant peak in the spectra of spanwise wavenumbers, which is of the same magnitude as the height of large microstructures. Furthermore, increasing the microstructure height weakens the streamwise correlation of the flow, and the characteristic scale of the correlation is comparable to the height of large microstructures.

Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow

In this study, we conduct a parametric analysis to evaluate the sensitivities of wall-modeled large-eddy simulation (LES) with respect to subgrid-scale (SGS) models, mesh resolution, wall boundary conditions and mesh anisotropy. While such investigations have been conducted for attached/flat-plate flow configurations, systematic studies specifically targeting turbulent flows with separation are notably sparse. To bridge this gap, our study focuses on the flow over a two-dimensional Gaussian-shaped bump at a moderately high Reynolds number, which involves smooth-body separation of a turbulent boundary layer under pressure-gradient and surface-curvature effects. In the simulations, the no-slip condition at the wall is replaced by three different forms of boundary condition based on the thin boundary layer equations and the mean wall-shear stress from high-fidelity numerical simulation to avoid the additional complexity of modeling the wall-shear stress. Various statistics, including the mean separation bubble size, mean velocity profile, and dissipation from SGS model, are compared and analyzed. The results reveal that capturing the separation bubble strongly depends on the choice of SGS model. While simulations approach grid convergence with resolutions nearing those of wall-resolved LES meshes, above this limit, the LES predictions exhibit intricate sensitivities to mesh resolution. Furthermore, both wall boundary conditions and the anisotropy of mesh cells exert discernible impacts on the turbulent flow predictions, yet the magnitudes of these impacts vary based on the specific SGS model chosen for the simulation.

Control of flow separation over an aerofoil by external acoustic excitation at a high Reynolds number

The effectiveness of acoustic excitation as a means of flow control at high Reynolds number turbulent flows is investigated numerically by using improved delayed detached eddy simulations (IDDES). Previous studies on low Reynolds number laminar flows have shown that acoustic excitation can substantially suppress flow separation for specific effective frequency and amplitude ranges. However, the effect of acoustic excitation on higher Reynolds number turbulent flow separation has not yet been explored due to limitations on appropriate fidelity computational methods or experimental facility constraints. Therefore, this paper addresses this research gap. A NACA0015 airfoil profile at 1 × 106 Reynolds number based on the airfoil chord length is used for the investigations. Acoustic excitation is applied to the baseline flow field in the form of transient boundary conditions at the computational domain inlet. A parametric study revealed that the effective sound frequency range shows a Gaussian distribution around the frequency of the dominant disturbances in the baseline flow. A maximum of ∼43% increase in lift-to-drag ratio is observed for the most effective excitation frequency F+=1.0 at a constant excitation amplitude of Am=1.8%. The effect of excitation amplitude follows an asymptotic trend with a maximum effective excitation amplitude above which the gains are not significant. A fully reattached flow is observed for the highest excitation level considered (Am=10%) that results in ∼120% rise in airfoil lift-to-drag coefficient. Overall, the findings of the current work demonstrate the higher Reynolds number effectiveness of acoustic excitation on separated turbulent flows, thereby paving the way for application in realistic flow scenarios observed in aircraft and gas turbine engine flow fields.

Numerical Simulation of Supersonic Turbulent Separated Flows Based on k–ω Turbulence Models with Different Compressibility Corrections

The accurate prediction of supersonic turbulent separated flows involved in aerospace vehicles is a great challenge for current numerical simulations. Based on the k–ω equations, several different compressibility corrections are incorporated in turbulence models to improve their prediction capabilities. Two benchmark test cases, namely the ramped cavity and the compression corner, are adopted for the numerical validation. Detailed comparisons between simulations and experiments are conducted to evaluate the effect of compressibility corrections on turbulence models. The computed results indicate that compressibility corrections have a significant impact on turbulence model performance. The compressibility correction, considering the effects of both dilatation dissipation and pressure dilatation, is suitable for the prediction of compressible free shear layers, but it may have a negative impact on the prediction of low-speed flows in the near-wall region due to the severe underprediction of the wall skin friction coefficient. In comparison, the compressibility correction only considering the effects of dilatation dissipation is conservative, with decreased predictability of free shear layers in supersonic flows, although it improves the predictions of the original models without corrections.

Numerical Study of the Influence of the Critical Reynolds Number on the Aerodynamic Characteristics of the Wing Airfoil

The paper reports the results of a study concerned with the influence of the size of the leading edge laminar bubble on the aerodynamic characteristics of the HGR01 airfoil. The completely turbulent and transient flows are considered. The mechanism of the appearance and interaction of laminar and turbulent flow separation near the leading and trailing edges of the airfoil is studied in detail. In the paper, the dependence of aerodynamic forces on the critical Reynolds number for the HGR01 airfoil is discussed. It has been established that the separation bubble at the leading edge can only be obtained using the laminar–turbulent transition model. Fully turbulent models are not able to show this feature of the airfoil flow. Graphs of the lift coefficient as a function of the critical Reynolds number, as well as the pressure distribution as a function of the size of the laminar bubble, are shown.

Blockage ratio and Reynolds number effects on flows around a rectangular prism

The combined effects of blockage ratio (BR) and Reynolds number (Re) on the spatiotemporal characteristics of turbulent flow separation around a rectangular prism with depth-to-thickness ratio of 3 were investigated using a time-resolved particle image velocimetry. Four different blockage ratios (BR = 2.5%, 5%, 10%, and 15%) were examined at Reynolds numbers of 3000, 7500, and 15000. Two regimes (unattached and reattached) were identified; however, the boundary between these regimes shows a complex dependency on BR and Re. The mean flow does not reattach onto the prism at low BR and Re but tends to reattach when BR and Re increase. The wake vortices are relatively larger for the unattached test cases. The separation bubbles over and in the wake of the prism are dynamically coupled for prisms in the unattached regime but independent of each other in the reattached regime. Spectral analyses of the velocity fluctuations and coefficient of the first proper orthogonal decomposition mode pair reveal a single dominant peak at the same fundamental shedding frequency for the reattached test cases, whereas multiple competing frequencies are observed for test cases in the unattached regime. The Kelvin–Helmholtz frequency increases with an increase in BR and Re. The vortical structures are more organized for prisms in the reattached regime, and their convective velocities in the wake are comparatively higher.

Capturing the drag crisis in the flow around a smooth cylinder using a hybrid RANS-LES model on coarse meshes

A hybrid strategy combining Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) methods is nowadays seen as an efficient way to simulate turbulent flows of practical relevance. In this work, the scale-resolving hybrid (SRH) model proposed by Manceau (2018) is compared with a conventional unsteady RANS model, and LES and experimental data from the literature for the flow around a smooth cylinder in the flow regime around the drag crisis. Based on a temporal filtering formalism, this approach has seen limited testing for turbulent separated flows. The drag crisis phenomenon is dominated by complex near-wall physics and is challenging to simulate. The predictive accuracy and the robustness to mesh coarsening for the SRH model are assessed for this test case, with the aim to demonstrate that this hybrid approach can be a credible cost-saving alternative to LES for separated turbulent flows. The meshes considered in this numerical study are far coarser than the ones used in the LES reference data, yet, the results for the time mean drag are found in good agreement with the reference data. Other features of the flow, such as the presence and sizes of the laminar separation bubbles and the consequent magnitude of the time mean lift are not as well captured. In general, the qualitative behaviour of the SRH model is good when considered in the context of questions previously raised in the literature about hybrid models. The mesh savings are achieved by coarsening the spatial resolution in the wake, whereas the resolution required in the near-wall area and shear layers remains high, though much reduced compared to the reference LES data. The key point taken from this study is that the SRH model is an attractive option to produce higher-fidelity data on coarse meshes.

Combustion characteristics of line fire under cross wind: Effect of flow separation in the boundary layer

The line fire under cross wind is a fundamental combustion phenomenon which could occur in wildland and urban fires. This paper systematically investigates the effect on the linear flame behavior of the flow separation in the boundary layer, by experimental and numerical simulations. The effects of the distance between the burner rim and table's edge, the wind speed and the heat release rate (HRR) are considered on the linear flame. A reverse flame is experimentally and numerically observed along the upstream direction, due to the interaction between the flow separation and the burning flame. The flow velocity and pressure fields, given by the numerical simulation, clarify that the positive pressure difference derives the reverse flame from the burner surface to the upstream in the bottom of flow separation bubble. In addition, the reverse flame would heat the air in the whole boundary layer and accelerate the flow speed to enlarge the size of the separation bubble. Two different regimes that relate to the laminar and turbulent separated flows, respectively, are clarified for the reverse flame at a critical state. Dimensionless analysis is conducted to develop the critical criterion that distinguishes the appearance and disappearance of the reverse flame. In a fully turbulent separated flow, the pulsation frequency of the reverse flame at a critical state seems to equal the frequency of vortex shedding from the separation point. It is also demonstrated that the flow separation would affect the flame geometry by enhancing the air-fuel mixing in the bottom of flame.

Improved hybrid model for transitional separated flows over a rough compressor blade

It is known that boundary layer transition and turbulent separation flow after transition can be influenced significantly by surface roughness. Since the traditional hybrid RANS/LES method cannot predict the boundary layer transition, and the RANS-based transition model cannot accurately simulate the massively separated flow, the present study sought to build an effective modeling strategy for the laminar, roughness-induced-transition and attached turbulence/massively separated flows that couples the Very-Large-Eddy-Simulation (VLES) model and a transition model considering roughness effects. Because the hybrid function between the transition model and VLES model constructed in the previous version still has some flaws, there is still a large laminar flow indication area in the turbulent flow region, which will reduce the simulation accuracy of the turbulent flow after transition. In this paper, the hybrid function is improved, which is examined in the simulation of the high-subsonic flow around the V103 compressor blade. Our analysis shows that the new hybrid model operates in the flow around the V103 compressor blade. The predictions of laminar separation bubble-induced transition, separation evolution, and reattachment are in accord with measurements and the LES results over both smooth and rough surfaces, indicating that the present transitional VLES method can achieve the simulation accuracy close to the LES method while reducing the computational cost.

Experiments on axial-flow-induced vibration of a free-clamped/clamped-free rod for light-water nuclear reactor applications

The flow-induced vibration of a cantilever rod confined in a pipe and exposed to an axial water flow has been experimentally investigated using a simple test piece designed to be informative for water-cooled nuclear reactor fuel rods. The Reynolds number was varied between 7.43 k and 82.5 k: a range that significantly extends the scope of existing data. Measurements were carried out using non-contact techniques: fast video imaging was used to track the rod motion, whilst particle image velocimetry was employed to resolve the flow field. The sources of excitation that sustain the rod vibration include turbulent buffeting, movement-induced excitation, and flow separation at the rod tip, whilst the observed dynamic responses of the rod comprise a fuzzy period-1 motion, a flutter-like large-amplitude oscillation, and buckling. Since both the rod vibration and the flow field are measured, the present data are particularly suited for numerical methodology development and validation.

Temporal super-resolution using smart sensors for turbulent separated flows

Particle image velocimetry (PIV) data of high Reynolds number unsteady turbulent flows are often undersampled in time; this leads to aliasing of important spectral content. The present work proposes a novel data-driven estimation technique that uses oversampled sparsely placed surface-mounted pressure sensors and long short-term memory neural networks to resolve the aliased transient velocity dynamics from undersampled PIV data. The method leverages the time-resolved pressure dynamics to estimate the temporal evolution of a proper orthogonal decomposition-based low-dimensional subspace of the velocity field. The proposed approach is demonstrated on a PIV dataset of a high Reynolds number turbulent separated flow over a Gaussian speed-bump benchmark geometry ( $$\text{Re}_{H}=2.26\times 10^{5}$$ , where H is the Bump height). The 15 Hz PIV data is super-resolved to 2 kHz, and spectral analysis of the flowfields is conducted to educe the originally aliased unsteady dynamics of the turbulent separation bubble. The estimator is shown to accurately reconstruct the Reynolds shear stress from unseen sensor data, demonstrating its generalizability to resolve the coherent motions. The estimated velocity spectra show distributions consistent with those of other separated flows.

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.

Large-eddy simulation of separated turbulent flows over a three-dimensional hill using WRF and OpenFOAM

It is not clearly known about the limitations of the large-eddy simulation (LES) mode of an atmospheric model (WRF) in predicting the microscale flows for engineering purpose. This study chooses a typical separated turbulent flow past a three-dimensional axisymmetric hill and investigates the performance of WRF-LES in comparison with the popular CFD solver (OpenFOAM). The numerical models and conditions are set similarly between the two codes. The instantaneous visualization shows that both WRF-LES and OpenFOAM-LES can produce the primary flow features, including hairpin vortices, horseshoes, and surface-shear-induced vortices at different scales, with high similarity. Nevertheless, the turbulent kinetic energy in the near wake produced by WRF-LES is underestimated, in comparison with WRF-LES. The energy spectra suggest that WRF-LES using the high-order advection schemes has a stronger capacity of generating and maintaining small-scale turbulent motions than OpenFOAM-LES. Furthermore, the deviation of numerical dissipation behavior is examined between the two solvers.

Cluster-based control for net drag reduction of the fluidic pinball

We propose a Cluster-Based Control (CBC) strategy for model-free feedback drag reduction with multiple actuators and full-state feedback. CBC consists of three steps. First, the input of the feedback law is clustered from unforced flow data. Second, the feedback law is interpolated with actuation commands associated with the cluster centroids. Thus, centroids and these actuation commands facilitate a low-dimensional parameterization of the feedback law. Third, the centroid-based actuation commands are optimized, e.g., with a downhill simplex method. This framework generalizes the feature-based CBC from Nair et al. [“Cluster-based feedback control of turbulent post-stall separated flows,” J. Fluid Mech. 875, 345–375 (2019)] in three aspects. First, the control law input is the velocity field. Second, the control law output commands multiple actuators here. Third, a reformulation of the downhill simplex method allows parallelizing the simulations, thus accelerating the computation threefold. Full-state CBC is demonstrated on a multiple-input configuration, the so-called fluidic pinball in three flow regimes, including symmetric periodic at Re = 30, asymmetric periodic at Re = 100, and chaotic vortex shedding at Re = 150. The net drag reductions for the three cases amount to 33.06%, 24.15%, and 12.23%, respectively. CBC shows distinct advantages for robustness control at different flow conditions. The full-state CBC further reveals the evolution of the control flow associated with the centroids, which contributes to the physical interpretation of the feedback control process.

Discovering explicit Reynolds-averaged turbulence closures for turbulent separated flows through deep learning-based symbolic regression with non-linear corrections

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier–Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize the paradigm of turbulence modeling. However, due to the black-box essence of most ML methods, it is currently hard to extract interpretable information and knowledge from data-driven models. To address this critical limitation, this work leverages deep learning with symbolic regression methods to discover hidden governing equations of Reynolds stress models. Specifically, the Reynolds stress tensor is decomposed into linear and non-linear parts. While the linear part is taken as the regular linear eddy viscosity model, a long short-term memory neural network is employed to generate symbolic terms on which tractable mathematical expressions for the non-linear counterpart are built. A novel reinforcement learning algorithm is employed to train the neural network to produce best-fitted symbolic expressions. Within the proposed framework, the Reynolds stress closure is explicitly expressed in algebraic forms, thus allowing for direct functional inference. On the other hand, the Galilean and rotational invariance are craftily respected by constructing the training feature space with independent invariants and tensor basis functions. The performance of the present methodology is validated through numerical simulations of three different canonical flows that deviate in geometrical configurations. The results demonstrate promising accuracy improvements over traditional RANS models, showing the generalization ability of the proposed method. Moreover, with the given explicit model equations, it can be easier to interpret the influence of input features on generated models.

Artificial neural network-based wall-modeled large-eddy simulations of turbulent channel and separated boundary layer flows

Wall-models in a large-eddy simulation (LES) are essential to alleviate the large near-wall resolution requirements for high-Reynolds-number turbulent flow simulations. Among the existing wall-models for a LES, an equilibrium wall-stress model has the highest computational efficiency. Because this model has limitations, such as a lack of non-equilibrium effects and the assumption of a particular law of the wall in the mean velocity, we propose artificial neural network-based wall-stress models (AWMs). The input variables for the AWMs are extracted from the decomposition of the skin-friction coefficient proposed by Fukagata et al. [1], and the AWMs are shown to be able to predict the wall-shear stress in complex flows accurately. The performance of the AWMs is tested for two types of flows, a fully developed turbulent channel flow and a separated turbulent boundary layer flow. A direct comparison of the turbulence statistics with those obtained by previous wall-models (i.e., a log-law-based wall-stress model and a non-equilibrium wall-stress model) shows that better predictions are achieved using the AWMs for both flows, even with untrained Reynolds numbers. When using a coarse grid along the wall-normal direction in wall-modeled LESs (WMLESs) with the AWMs, an upward shift of the mean velocity profile (positive log-layer mismatch, LLM) compared to direct numerical simulation data is found, consistent with previous studies. However, this LLM problem can be overcome by imposing a filtered wall-normal velocity at the wall that is dynamically determined based on the continuity equation and the Taylor series expansion within wall-adjacent cells.

Wall-Resolved Large-Eddy Simulation of Near-Stall Airfoil Flow at

A wall-resolved large-eddy simulation (LES) of the near-stall flow around the Aerospatiale A-airfoil at is conducted. The present LES shows typical Reynolds-number effects compared to the previous LES at , such as the increase in lift coefficient, decrease in boundary-layer thickness, delay of turbulent flow separation, and upstream shift of transition location. Among these Reynolds-number effects, the difference in the development of momentum displacement thickness is focused on and further analyzed based on the integral relation of the boundary layer. This analysis reveals that the different mechanisms of the laminar–turbulent transition between the two Reynolds-number cases cause an initial difference in the momentum displacement thickness. This initial difference is then amplified downstream by the deceleration effects of the mean flow. These results suggest that proper estimation of the laminar and transitional flows near the leading edge is crucial for predicting the trailing-edge stall phenomena and their dependency on the Reynolds number.