Strong Adverse Pressure Gradient Research Articles

New momentum integral equation applicable to boundary layer flows under arbitrary pressure gradients

By incorporating the traditionally overlooked advective term in the wall-normal momentum equation, a new momentum integral equation is developed for two-dimensional incompressible turbulent boundary layers under arbitrary pressure gradients. The classical Kármán's integral arises as a special instance of the new momentum integral equation when the pressure gradient is weak. The new momentum integral equation's validity is substantiated by direct numerical simulation data. Unlike the classical Kármán's integral, which is limited to predicting wall shear stress within mild pressure gradients, the new momentum integral equation accurately computes wall shear stress across a broad range of pressure gradients, even in the presence of strong adverse pressure gradients that lead to flow separation. Moreover, a new pressure parameter $\beta _\kappa$ is introduced through examining terms in the new momentum integral equation. This parameter naturally quantifies the pressure gradient's influence on turbulent boundary layers and offers guidance for applying the classical Kármán's integral. Additionally, to facilitate experimental determination of wall shear stress under strong pressure gradients, an approximate integral equation is proposed that relies solely on easily measurable variables. Validation against direct numerical simulation data demonstrates that this simplified equation provides reasonably accurate estimates of wall shear stress in turbulent boundary layers experiencing strong pressure gradients.

Modal analysis of vortex rope using dynamic mode decomposition

The decelerating swirling flow in the draft tube of hydraulic turbines at part load conditions often results in a self-induced instability known as vortex rope. This phenomenon is associated with detrimental pressure pulsations in the hydropower system that need to be mitigated. A deep understanding of such instability is essential for developing effective mitigation and control strategies. The current article exploits the dynamic mode decomposition (DMD) algorithm to perform an in-depth modal analysis of the physical aspects of the vortex rope. DMD can efficiently identify distinct coherent structures with isolated frequencies. The sparsity-promoting variant of DMD is exploited to extract the most influential modes. The computational fluid dynamics (CFD) data is generated via a resolved improved delayed detached eddy simulation using OpenFOAM. Frequency analysis of the CFD data uncovered peaks at the normalized frequencies of f/fn=0.56 and 0.63, whose origins seemed initially unclear. Nevertheless, the DMD modal analysis elucidates that these excitations are associated with the rotation of the reunited vortex and fluctuations of the separated boundary layer, respectively. The non-linear dynamics of the flow field are unveiled through a modal decomposition revealing distinctive coherent structures with isolated frequencies. These include rotational and plunging modes of the vortex rope, traveling wakes of the blades, boundary layer separation due to strong adverse pressure gradient, and a reunited vortex core. The flow field reconstruction through time dynamics of DMD modes highlights while it is possible to achieve a perfect flow field reconstruction considering all recovered modes, the model typically fails to predict future behavior with an acceptable level of accuracy. The chaotic nature of the resolved turbulent flow field presents a substantial challenge for predicting the future through a model built based on prior events. The current modal analysis not only provides a more comprehensive understanding of the physics underlying the vortex rope phenomenon but also lays the groundwork for potential future applications in controlling mechanisms.

Improved prediction of turbomachinery flows using Reynolds stress model with [formula omitted] transition model

Transition is a prominent flow phenomenon in turbomachinery, especially at low and moderate Reynolds numbers. The turbomachinery internal flow often encounters complex vortex structures, typically accompanied by strong turbulence anisotropy and non–equilibrium. Conventional Reynolds–averaged Navier–Stokes (RANS) modeling with linear eddy–viscosity models (LEVMs) may fail short in capturing certain complex flow features. The Reynolds stress model (RSM) based on a higher turbulence closure level has more potential to reasonably consider turbulence anisotropy and non–equilibrium for such complex flows within turbomachinery than the LEVMs. However, the current RSM lacks an effective representation of transition phenomena. This paper presents an improved prediction of turbomachinery flows using RSM with transition modeling. The transition effects are incorporated into the RSM (SSG/LRR–ω model) via Menter's γ transport equation. The blending of the SSG/LRR–ω model with the γ transition model (SSG/LRR–ω–γ model) is firstly validated based on the T3 series flat plate cases with zero pressure gradient (T3A, T3B, T3A–) and variable pressure gradients (T3C1–C5). Comparisons with experiments show that the SSG/LRR–ω–γ model predicts corner separation flows with transition more accurately, although there is still room for further improvement. Then, the performance of the SSG/LRR–ω–γ model is assessed in a linear highly loaded prescribed velocity distribution (PVD) cascade and a NACA65 K48 compressor cascade. Comparisons with experiments indicate that, in both compressor cascades, the SSG/LRR–ω–γ model can predict more accurately corner flows with boundary layer transition on suction surfaces than the SSG/LRR–ω and SST model. Nevertheless, it still exhibits a tendency to overestimate the size of corner separation, especially in cases characterized by strong adverse pressure gradients. Comparisons of skin friction and velocity profiles predicted by the SSG/LRR–ω model with and without transition modeling illustrate the rationale behind the improved prediction. Further improvement of the SSG/LRR–ω–γ model for predicting turbomachinery corner flows should be conducted in future.

Unsteady Cloud Cavitation on a 2D Hydrofoil: Quasi-Periodic Loads and Phase-Averaged Flow Characteristics

We perform large-eddy simulations to study a cavitating flow over a two-dimensional hydrofoil section—a scaled-down profile (1:13.26) of guide vanes of a Francis turbine—using the Schnerr–Sauer cavitation model with an adaptive mesh refinement in intensive phase transition flow areas. In the test case, the guide vane is tilted at an angle of attack of 9° to the direction of the flow, in which the Reynolds number, based on the hydrofoil chord length, equals 1.32×106, thus providing a strong adverse pressure gradient along the surface. The calculated time-averaged turbulence characteristics are compared with those measured by particle image velocimetry to verify that the flow is correctly reproduced in numerical simulations using the procedure of conditional averaging proposed and tested in our previous investigation. A re-entrant jet is identified as the primary source of vapor cloud shedding, and a spectral analysis of the cavitating flow over the profile midsection is conducted. Two characteristic frequencies corresponding to the cases, when an attached cavity detaches completely (as a whole) and two partially from the hydrofoil, are found in the flow. The study reveals that the natural frequency of partial cavity shedding is three times higher than that of full detachments. The examined regime exhibits an oscillatory system with two oscillation zones related to cavitation surge instability and unsteady cloud cavitation resulting from the re-entrant jet. Conditional averaging correlates cavitation structures with pressure distributions, forces, and torque on the guide vane. This modeling approach captures the fine details of quasi-periodic cavitation dynamics, providing insights into unsteady sheet/cloud cavitation and offering a method for developing control strategies.

Simulation of High-Enthalpy Turbulent Shock Wave/Boundary Layer Interaction Using a RANS Approach

In the era of space exploration, the scientific community is strongly focusing on the analysis of hypersonic flows in the presence of shock wave/boundary layer interaction. In these conditions, the flow field presents a complex shock structure due to the interaction of different shock waves with the boundary layer. The strong adverse pressure gradient makes the boundary layer separate, giving rise to a separation bubble. In the reattachment zone, the temperature can reach very high values, inducing thermochemical non-equilibrium effects. This research field is recently achieving more and more relevance in aerospace research, as the analysis of turbulent shock wave/boundary layer interaction so far has been mainly focused on perfect gas flows. In this manuscript, a Reynolds averaged Navier–Stokes (RANS) approach is considered, the shear stress transport (SST) model being coupled with the multitemperature approach proposed by Park to investigate thermochemical non-equilibrium effects in hypersonic turbulent shock wave/boundary layer interaction. The first part of the manuscript is devoted to the validation of the solver, and results for low enthalpy flat plate and compression ramp flows are presented. The numerical results are shown to be in good agreement with numerical solutions and experimental measurements. Afterward, the free stream conditions are modulated to make non-equilibrium relevant and analyze a reacting flow.

Scale-Resolving Hybrid RANS-LES Simulation of a Model Kaplan Turbine on a 400-Million-Element Mesh

Double-regulated Kaplan turbines with adjustable guide vanes and runner blades offer a high degree of flexibility and good efficiency for a wide range of operating points. However, this also leads to a complex geometry and flow guidance with, for example, vortices of different sizes and strengths. The flow in a draft tube is especially challenging to simulate mainly due to flow phenomena, like swirl, separation and strong adverse pressure gradients, and a strong dependency on the upstream flow conditions. Standard simulation approaches with RANS turbulence models, a coarse mesh and large time step size often fail to correctly predict performance and can even lead to wrong tendencies in the overall behavior. To reveal occurring flow phenomena and physical effects, a scale-resolving hybrid RANS-LES simulation on a block structured mesh of about 400 million hexahedral elements of a double-regulated five-blade model Kaplan turbine is carried out. In this paper, first, the results of the ongoing simulation are presented. The major part of the simulation domain is running in LES mode and seems to be properly resolved. The validation of the simulation results with the experimental data shows mean deviations of less than 0.8% in the global results, i.e., total head and power, and a good visual agreement with the three-dimensional PIV measurements of the velocity in the cone and both diffuser channels of the draft tube. In particular, the trend of total head and the results for the draft tube differ significantly between the scale-resolving simulation and a standard RANS simulation. The standard RANS simulation exhibits a highly unsteady behavior of flow, which is not observed in the experiments or scale-resolving simulation.

Direct numerical simulation of thermal turbulence in an aero-engine blade channel

The flow and heat-transfer phenomena are simulated by direct numerical simulation in the NACA65 blade channel with a Reynolds number equaling to 1.367×105. Induced by the strong adverse pressure gradient, the flow separations are observed on the suction surface with the multi-scale and multi-layer vortices. The DNS results indicates that the backflow transition is triggered by the small-scale spanwise-vortex fluctuations due to the viscous linear instability, and thereafter is further stretched into the quasi-streamwise vortices due to the upper K-H rolls, which generates the typical coherent structures in the flow-separation region. The Reynolds shear stresses and turbulent heat flux are found very strongly and actively concentrating in the region bounded by the blade-wall and the upper boundary of separation where the variety of ejections and sweeps are observed. These ejections and sweeps promote the momentum and heat transfers, which results in the large temperature gradients in both the near-wall and flow-separation regions. Moreover, the separation and reattachment zones present the non-similarity distributions for both the wall-normal heat flux and Reynold shear stresses due to the strong adverse pressure gradient. Therefore, the diverse profiles of velocity and temperature can be found developing in streamwise along the suction surface. However, through applying the newly-developed wall-bounded law formulations, it is demonstrated that these wall-laws are even universally capable of accurately representing these diverse velocity and temperature profiles.

A study of the effect of curvature and pressure gradient on aerodynamics performance and turbulence structure of S-shaped compressor transition duct

ABSTRACT The overall performance of the high-pressure compressor in a turbofan engine entirely depends on the flow supplied by the upstream transition duct. A robust and efficient design of the transition duct conveys a highly uniform flow with minimum pressure loss. The present study aimed to determine the effect of adverse pressure gradient and curvature on the flow of the compressor duct. The results suggest that the outer wall curvature causes a significant decrease in from +0.19 to −0.6, and as a result, 75% length of the outer wall is suspended in the favourable pressure gradient. On the contrary, it increases from −0.54 to +0.14 along the inner wall. It implies that most of the inner wall lies in the adverse pressure gradient; consequently, the turbulence structure, mean flow behaviour, and Reynolds stresses are considerably modified. The presence of a strong adverse pressure gradient significantly enhances turbulence quantities along the inner wall. Additionally, the boundary layer parameters grow relatively thicker along the inner wall than on the outer wall. As a result, a considerable increase in the shape parameter (H = 2.12) is obtained.

Turbulent superstructure statistics in a turbulent boundary layer with pressure gradients

In turbulent boundary layers, streamwise elongated regions of high- and low-momentum in the log-law layer that can extent up to several boundary layer thicknesses are often referred to as turbulent superstructures. These structures contain a relatively large portion of the layer’s turbulent kinetic energy and have been shown to interact with the near-wall flow structures. In the last few decades extensive research on zero-pressure gradient (ZPG) turbulent boundary layers has been done, however by comparison, the structural characteristics for adverse pressure gradient turbulent (APG) boundary layer flows are much less studied despite their strong significance aero-hydrodynamic vehicle design. Therefore, the three-dimensional dynamics of turbulent superstructures in a turbulent boundary layer flow are investigated in the Atmospheric Wind Tunnel Munich (AWM) using a multi-camera 3D time-resolved Lagrangian particle tracking approach. In this study, Lagrangian and Eulerian statistics will be used to characterize the dynamics and interaction of turbulent superstructures within a zero pressure gradient (ZPG) turbulent boundary layer at Reτ = 5000 or Reθ = 14 000 that then flows over a curved plate subjected to a favorable (FPG) and strong adverse (APG) pressure gradient, which eventually separates. An Eulerian analysis, using multi-point correlations of 3D velocity fields, found that the average superstructure topology is modulated by decelerating flow in the APG region when compared to the ZPG region, however the basic shape and spanwise pattern is preserved. Looking into the behavior of individual trajectories, it was found that the dispersion of single particles along trajectories in the log-law layer are capable of moving more than the average Eulerian superstructure spacing in the spanwise direction. Furthermore, the mean square of the single particle dispersion indicates that the maximum dispersion in the spanwise direction comes from particles released at the wall-normal location corresponding to the so-called “second-peak/plateau” region in the streamwise normal Reynolds stress.

On the extension of k−ω−SST corrections to predict flow separation on thick airfoils with leading‐edge roughness

AbstractModern wind turbines employ thick airfoils in the outer region of the blade with strong adverse pressure gradients and high sensitivity to flow separation, which can be anticipated by leading‐edge roughness. However, Reynolds average Navier‐Stokes simulations currently overpredict the Reynolds shear stresses near the surface, and the flow separation is not correctly predicted. Hence, these methods are not representative enough to optimize the blade design to avoid flow separation, which becomes relevant for rough blades. While several eddy‐viscosity corrections in the turbulence model have been previously studied to predict flow separation over smooth airfoils, the present study aims to extend their applicability to airfoils with leading‐edge roughness. Two corrections, whose effect on flow physics has not been empirically quantified, are addressed. Particle image velocimetry measurements have been performed on a 30% thick airfoil to quantify the impact of these corrections. The reduction of the eddy viscosity introduced by the corrections leads to a shift of the peak location of the Reynolds shear stresses away from the surface, which, in turn, promotes flow separation and improves the prediction of the mean velocity and the pressure‐coefficient distribution. Besides, the ratio between the main turbulent shear stress and turbulent kinetic energy is demonstrated to be lower than the standard value used in the turbulence model at the boundary‐layer outer edge. Adjusting this ratio for an angle of attack of 0° decreases the error on the predicted lift and drag coefficients from 75% to 3% and from 58% to 39%, respectively.

Wall-pressure fluctuations in an axisymmetric boundary layer under strong adverse pressure gradient

Measurements of fluctuating wall pressure in a high-Reynolds-number flow over a body of revolution are described. With a strong axial pressure gradient and moderate lateral curvature, this non-equilibrium flow is relevant to marine applications as well as short-haul urban transportation. The wall-pressure spectrum and its scaling are discussed, along with its relation to the space–time structure. As the flow decelerates downstream, the root-mean-square level of the pressure drops together with the wall shear stress ( $\tau _w$ ) and is consistently approximately 7 $\tau _w$ . While the associated dimensional spectra see a broadband reduction of over 15 dB per Hz, they appear to attain a single functional form, collapsing to within 2 dB when normalized with the wall-wake scaling where $\tau _w$ is the pressure scale and $U_e/\delta$ is the frequency scale. Here, $\delta$ is the boundary layer thickness and $U_e$ is the local free-stream velocity. The general success of the wall-wake scaling, including in the viscous $f^{-5}$ region, suggests that the large-scale motions in the outer layer play a predominant role in the near-wall turbulence and wall pressure. On investigating further, we find that the instantaneous wall-pressure fluctuations are characterized by a quasi-periodic feature that appears to convect downstream at speeds consistent with the outer peak in the turbulence stresses. The conditional structure of this feature, estimated through peak detection in the time series, resembles that of a roller, supporting the embedded shear layer hypothesis (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642; Balantrapu et al., J. Fluid Mech., vol. 929, 2021, A9). Therefore, the outer-region shear-layer-type motions may be important when devising strategies for flow control, drag and noise reduction for decelerating boundary layers.

Effect of inclination angle on the film cooling in a serpentine nozzle with strong adverse pressure gradient

The serpentine nozzle is widely used in military unmanned aerial vehicles to improve their viability. The film cooling technology should be used in the serpentine nozzle to cope with excessive thermal load. Strong adverse pressure gradient (APG) in the serpentine nozzle induces the recirculation zone near the upper wall downstream of the film hole, such that the effect of inclination angle on the film cooling characteristics is quite different from that in other studies. A numerical investigation was conducted to study the influence of the film hole inclination angle (α = 20°, 30°, 45°, 60°) on the film cooling characteristics in a serpentine nozzle with strong APG. Results show that the inclination angle changes the region of recirculation zone, then affects the development of counter rotating vortex pair and anti-counter rotating vortex pair (ACRVP), and finally results in different distributions of the film cooling effectiveness (FCE). For blowing ratio, M, = 0.5, 1, and 1.5, with the increase in the inclination angle, the recirculation zone expands, and the vorticity of the ACRVP increases. For M = 2, with the increase in the inclination angle, the recirculation zone first shrinks and then expands, and the vorticity of the ACRVP first decreases and then increases. Taking all the four blowing ratios into account, we find that the 30° inclination angle gives the best film cooling effect, and the area-average FCE under conditions α = 20°, α = 45°, and α = 60° is 7.5%, 5.6%, and 5.0%, respectively, lower than that under condition α = 30°. Therefore, the 30° inclination angle is the optimal choice for the film holes near the APG region of the serpentine nozzle.

Outer scaling of the mean momentum equation for turbulent boundary layers under adverse pressure gradient

A new scaling of the mean momentum equation is developed for the outer region of turbulent boundary layers (TBLs) under adverse pressure gradient (APG). The maximum Reynolds shear stress location, denoted as $y_{m}$ , is employed to determine the proper scales for the outer region of an APG TBL. An outer length scale is proposed as $\delta _e - y_{m}$ , where $\delta _e$ is the boundary layer thickness. An outer velocity scale for the mean streamwise velocity deficit is proposed as $U_e - U_{m}$ , where $U_e$ and $U_m$ are the mean streamwise velocities at the boundary layer edge and $y_{m}$ , respectively. An outer velocity scale for the mean wall-normal velocity deficit is proposed as $V_e - V_{m}$ , where $V_e$ and $V_{m}$ are the wall-normal velocities at $\delta _e$ and $y_{m}$ , respectively. The maximum Reynolds shear stress is found to scale as $(\delta _e - y_{m}) U_e \,{\rm d}U_e/{{\rm d}x}$ . The new outer scaling collapses well the experimental and numerical data on APG TBLs over a wide range of Reynolds numbers and strengths of pressure gradient. Approximations of the new scaling are developed for TBLs under strong APG and at high Reynolds numbers. The relationships between the new scales and previously proposed scales are discussed.

Influence of Cavitation on Unsteady Vortical Flows in a Side Channel Pump

Previous investigation on side channel pump mainly concentrates on parameter optimization and internal unsteady vortical flows. However, cavitation is prone to occur in a side channel pump, which is a challenging issue in promoting performance. In the present study, the cavitating flow is investigated numerically by the turbulence model of SAS combined with the Zwart cavitation model. The vapors inside the side channel pump firstly occur in the impeller passage near the inlet and then spread gradually to the downstream passages with the decrease of NPSHa. Moreover, a strong adverse pressure gradient is presented at the end of the cavity closure region, which leads to cavity shedding from the wall. The small scaled vortices in each passage reduce significantly and gather into larger vortices due to the cavitation. Comparing the three terms of vorticity transport equation with the vapor volume fraction and vorticity distributions, it is found that the stretching term is dominant and responsible for the vorticity production and evolution in cavitating flows. In addition, the magnitudes of the stretching term decrease once the cavitation occurs, while the values of dilatation are high in the cavity region and increase with the decreasing NPSHa. Even though the magnitude of the baroclinic torque term is smaller than vortex stretching and dilatation terms, it is important for the vorticity production along the cavity surface and near the cavity closure region. The pressure fluctuations in the impeller and side channel tend to be stronger due to the cavitation. The primary frequency of monitor points in the impeller is 24.94 Hz and in the side channel is 598.05 Hz. They are quite corresponding to the shaft frequency of 25 Hz (fshaft = 1/n = 25 Hz) and the blade frequency of 600 Hz (fblade = Z/n =600 Hz) respectively. This study complements the investigation on cavitation in the side channel pump, which could provide the theoretical foundation for further optimization of performance.

Turbulence structure under the free-surface wave around an advancing surface-piercing cylindrical body

Free-surface wave effects on the turbulent boundary layer and wake of a surface-piercing slender body are investigated by measuring the flow and free-surface elevation around the model in three different Froude number (Fr) conditions—0.126, 0.282, and 0.400. The flow is measured by a towed underwater stereoscopic particle image velocimetry system. At the lowest Fr of 0.126, there appears no significant wave pattern, but the flow retards under the free-surface. The free-surface hinders the flow underneath, as the solid surface does. The steady and smooth free-surface wave generated at the intermediate Fr of 0.282 affects the pressure gradient on the turbulent boundary layer. The momentum thickness increases due to the adverse pressure gradient from the wave trough to the wave crest. At the highest Fr of 0.400, a strong adverse pressure gradient results in flow separation and violent wave breaking. The wave-induced separation at the high Froude number condition stimulates momentum transfer and turbulence dissipation, resulting in isotropic turbulence.

Boundary Layer Transition Prediction on Planar Turbine Cascade Using Temperature-Sensitive Paint and Numerical Simulation

Advanced measurement technology on boundary layer transition is an effective means to study the flow mechanism and the performance of the cascade. In this research, to investigate the boundary layer transition of transonic VKI-RG turbine cascade, a noncontact measurement technique named temperature-sensitive paint (TSP) that is capable of quantitatively measuring the surface temperature of a model is used. Under the conditions of outlet Mach number (Ma2) = 0.4, 1.03, and 1.2, the transitional location of a cascade is accurately measured by TSP technique. Moreover, a numerical study on the transitional location of a planar cascade was conducted with the conditions of Mach number (Ma) and attack angle (α). The numerical results show that the transitional location moved forward with the increase in Ma2 and α at Ma2 < 1; otherwise, the transitional location moved backward with increasing Ma2 (Ma2 > 1). Lastly, a strong adverse pressure gradient was formed behind the shock wave, which led to the beginning of the transition.

Profile Loss Reduction of High-Lift Turbine Blades With Rough and Ribbed Surfaces

Abstract Transitional boundary layers on low-pressure turbines (LPTs) are prone to separation on the suction surface of the blade under strong local adverse pressure gradients. Intermittent freestream turbulence, periodic wakes shed by the upstream blades, and surface roughness due to in-service degradation of the blades are shown to suppress the separation. Although this generally leads to a profile loss reduction, some of the benefits are offset by a loss increase associated with an increased turbulent wetted area. In this work, we explore a strategy where the losses in both the transitional and turbulent boundary layers can be reduced. In particular, we employ surface roughness in the transitional regime to reduce the separation bubble-related losses and riblets in the turbulent regime to further reduce the losses due to the turbulent wetted area. The efficacy of this ‘rough-riblet blade surface’ is studied using high-fidelity eddy resolving simulations on the configuration of a flat surface subjected to streamwise varying pressure gradients. Two riblet shapes, sawtooth and scalloped, are considered. When compared to the roughness alone configuration, scalloped riblets reduced the skin friction drag by ≈10% and are much more effective than the sawtooth riblets. Through the streamwise evolution of the boundary layer parameters such as trailing edge momentum thickness, maximum turbulent kinetic energy, and Reynolds stresses, the additional losses incurred at the junction between the smooth wall and riblet leading edge are highlighted.

Depth effects on the cavity induced transition at hypersonic speed by DNS

Cavity-induced transition (CIT) in a hypersonic boundary layer was simulated by employing direct numerical simulation (DNS). The upwind Roe scheme was discretized by high-order minimum dispersion and controllable dissipation (MDCD) reconstruction based on high-quality multi-block structured grids. The grid scale and time step are determined after evaluating the grid scale and nondimensional time step and comparing with the available measurements. Four depths, 1.0, 1.5, 2.0, and 2.5, multiplied by the baseline depth (D), are evaluated to determine their effects on the CIT on the wall after the cavity. The baseline is a typically “closed” cavity and the width of turbulent region at one cavity length downstream cavity (x = 2L) is 67 mm, caused by the strong adverse pressure gradient and horseshoe vortex instability. Typically, the other three are “open” cavities with no transition for the 1.5D cavity, a turbulent region width of 26 mm for the 2.0D cavity, and 45 mm for the 2.5D cavity at x = 2L were obtained after the cavity. Moreover, the relationship between the flow structures and a typical high heat flux region is explored. Reattachment supplies heat to the wall, and separation removes heat from the wall.

A driving mechanism of near-wall turbulence subject to adverse pressure gradient in a plane Couette flow

The effect of adverse pressure gradient (APG) on near-wall turbulence is studied, with a particular attention to the turbulence production mechanism. A plane turbulent Couette flow is considered for several values of constant APG in the lower wall region. A direct numerical simulation (DNS) in a large computational domain shows that turbulence near the lower wall continues to exist even at sufficiently large APGs. On increasing the APG, the cross-streamwise turbulence intensities increase, and the near-wall streaks gradually disappear. A linear analysis using the optimal transient growth indicates that the APG inhibits the generation of near-wall streaks due to the significant reduction of the mean shear in the region near the lower wall. The turbulent fluctuation dynamics beyond the linear regime is studied with a DNS in a minimal flow unit. The near-wall self-sustaining process involving streaks is significantly weakened or destroyed as APG increases, while the turbulent fluctuations become more isotropic and localised. Using a conditional averaging analysis, a new mechanism of near-wall turbulence production under strong APG is uncovered. This mechanism is initiated by the wall-normal nonlinear transport of an outer wall-normal velocity fluctuation to the near-wall region. The transported wall-normal velocity fluctuation is subsequently amplified via the Orr mechanism, resulting in the non-zero turbulence production involving spatially localised vortical structures. This mechanism is also confirmed by DNS of the flow in a large computational domain, where strong correlation between the wall-normal nonlinear transport and turbulence production is observed.

Artificial neural networks modeling of wall pressure spectra beneath turbulent boundary layers

We analyze and compare various empirical models of wall pressure spectra beneath turbulent boundary layers and propose an alternative machine learning approach using Artificial Neural Networks (ANNs). The analysis and the training of the ANN are performed on data from experiments and high-fidelity simulations by various authors, covering a wide range of flow conditions. We present a methodology to extract all the turbulent boundary layer parameters required by these models, also considering flows experiencing strong adverse pressure gradients. Moreover, the database is explored to unveil important dependencies within the boundary layer parameters and to propose a possible set of features from which the ANN should predict the wall pressure spectra. The results show that the ANN outperforms traditional models in adverse pressure gradients, and its predictive capabilities generalize better over the range of investigated conditions. The analysis is completed with a deep ensemble approach for quantifying the uncertainties in the model prediction and integrated gradient analysis of the model sensitivity to its inputs. Uncertainties and sensitivities allow for identifying the regions where new training data would be most beneficial to the model's accuracy, thus opening the path toward a self-calibrating modeling approach.