Wave Boundary Layer Research Articles

Impact of Elevated Kelvin–Helmholtz Billows on the Atmospheric Boundary Layer

AbstractThe impact of Kelvin–Helmholtz billows (KHBs) in an elevated shear layer (ESL) on the underlying atmospheric boundary layer (BL) is examined utilizing a group of large-eddy simulations. In these simulations, KHBs develop in the ESL and experience exponential growth, saturation, and exponential decay stages. In response, strong wavy motion occurs in the BL, inducing rotor circulations near the surface when the BL is stable. During the saturation stage, secondary instability develops in the ESL and the wavy BL almost simultaneously, followed by the breakdown of the quasi-two-dimensional KH billows and BL waves into three-dimensional turbulence. Consequently, during and after a KH event, the underlying BL becomes more turbulent with its depth increased and stratification weakened substantially, suggestive of significant lasting impact of elevated KH billows on the atmospheric BL. The eventual impact of KHBs on the BL is found to be sensitive to both the ESL and BL characteristics.

Approximate velocity formula over mobile sediment bed induced by velocity-skewed waves and current

A velocity formula is proposed for flow over a mobile sediment bed induced by velocity-skewed waves and current. The formula is obtained by a separation of waves and current velocities and requires seven free variables related to free stream velocity and sediment characteristics. The formula includes two parts: (1) a wave part consisting of the free stream velocity and defect function, which considers phase lead, wave boundary layer thickness, and mobile bed level, and (2) a current part, which changes the wave part through the boundary layer thickness and mobile bed level, influenced by wave eddy viscosity. The wave part is superior to the current part such that the boundary layer characteristics are mainly determined by the waves. The wave process is divided into four quarter stages to model the asymmetries of parameters in velocity and acceleration. Under velocity-skewed waves and current conditions, velocity asymmetry and residual velocity are accounted for in the formula, especially the offshore residual velocity with a large phase lag and mobile bed effect with a small phase lag. Phase lead is shown to be non-constant in velocity-skewed oscillatory sheet flow and corresponds to an extra offshore residual velocity.

A modified defect function for wave boundary layers

In the present paper, a new defect function is proposed to predict the first harmonic motion in turbulent wave boundary layer (WBL) flows, based on the existing and newly acquired experimental evidences over a universal range of the governing flow parameters (A/ks &Re), taking the advantage of the existing defect function models. The defect function, denoted as D(z), having a complex form, describes the spatio-temporal velocity deficit in the WBL as the only function of z. For the new defect function, two sets of model parameters (p1 &λ1, p2 &λ2) are introduced to formulate the amplitude and phase defects, namely −ln|D|=(z/λ1)p1 and arg(D)=(z/λ2)p2. Correlation relationships between model parameters (p1 &λ1, p2 &λ2) and governing flow parameters (A/ks &Re) were established. Through (i) matching the logarithmic and the defect laws of velocity distribution and (ii) the ‘one particle analysis’ of turbulent diffusion process, we demonstrated that the model parameters λ1 and λ2 represent the characteristic length scales, and the model parameters p1 and p2 reflect the nonlinearities of amplitude defect and phase defect respectively. The new defect function not only leads to better predictions of the flow in the phase space than the existing models but also extends the applicable parameter ranges of the existing models.

Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

Impact of Shock Wave Boundary Layer Interaction on the Internal Flow and Performance of Scramjet Intake

Impact of Shock Wave Boundary Layer Interaction on the Internal Flow and Performance of Scramjet Intake

Characteristics of transition to turbulence over a Mach 6 flared cone

We study turbulence production at the end of a second-mode-induced transition in a Mach 6 boundary layer based on both experiments and numerical simulations. By using ultra-fast visualization and particle image velocimetry, we succeed in capturing a soliton-like wave packet that plays a determining role in turbulence production. We reproduce the experiment by direct numerical simulation, revealing that this wave packet arises from the vortical first Mack mode (the counterpart of Tollmien–Schlichting waves in low-speed boundary layers), rather than the rapidly growing dilatational second Mack mode, which triggers a Λ-vortex and consequent turbulent structure. These results reveal the existence of a transition mechanism in hypersonic boundary layers similar to that in low-speed boundary layers.

The effect of model material properties on thermal imaging measurements

The temperature distributions arising on the surface of the solid model are investigated. A flow with a shock wave and laminar boundary layer interaction is considered as the main flow. Calculations of the conjugate problem are performed based on RANS approach. The investigated cases correspond to homogeneous material of the solid model and the model consisting of two materials with different thermal conductivity. In this study, the model designs are found to obtain a temperature distribution suitable for thermal imaging measurements. In addition, in the calculations, the effect of forced heating of the model wall on the temperature distribution is investigated.

Investigation of Air-Sea Turbulent Momentum Flux over the Aegean Sea with a Wind-Wave Coupling Model

Near surface turbulent momentum flux estimates are performed over the Aegean Sea, using two different approaches regarding the drag coefficient formulation, a wave boundary layer model (referred here as KCM) and the most commonly used Coupled Ocean–Atmosphere Response Experiment (COARE) algorithm. The KCM model incorporates modifications in the energy-containing wave spectrum to account for the wave conditions of the Aegean Sea, and surface similarity to account for the stratification effects. Airborne turbulence data during an Etesian outbreak over Aegean Sea, Greece are processed to evaluate the simulations. KCM estimates found up to 10% higher than COARE ones, indicating that the wave-induced momentum flux may be insufficiently parameterized in COARE. Turbulent fluxes measured at about 150 m, and reduced to their surface values accounting for the vertical flux divergence, are consistently lower than the estimates. Under unstable atmospheric stratification and low to moderate wind conditions, the residuals between estimates and measurements are less than 40%. On the other hand, under stable stratification and strong winds, the majority of the residuals are more than 40%. This discrepancy is associated with the relatively high measurement level, shallow boundary layer, and the presence of a low level jet.

Control of shock‐induced separation inside air intake by vortex generators

AbstractThe present investigation is aimed towards the effect of passive methods on the performance of supersonic air intake along with the control of shock wave boundary layer interaction at various engine operating conditions. A computational study has been carried out in this regard using the commercially available software Ansys Fluent. The k–ω turbulence model has been selected for the present investigation. All the simulations have been carried out at a design Mach number of 2.2. The Independent effect of the air‐jet vortex generator (AJVG), tapered micro ramp vortex generator (MRVG), and the combined effect of AJVG with MRVG on the shock wave boundary layer interaction have been investigated. Detailed comparative studies of all controlled cases with uncontrolled cases show significant improvement in the flow field inside the air intake and improved performance. The shock train is also captured for all the cases along with shock wave boundary layer interaction at various operating conditions. The movement of the normal shocks is seen as the backpressure increases. All the essential performance parameters related to air intake have been examined in detail. The hybrid type of control showed better performance.

Mean Current Profile over Rippled-Beds in the Presence of Non-Breaking Waves and Analysis of Its Influencing Factors

Classical eddy viscosity model deviates from the actual mean current profiles, when calculating the mean current profiles over rippled-beds in the presence of non-breaking waves, owing to the neglect of the enhancement of the wave boundary layer thickness by ripples and the wave-induced shear stress (the radiation stress and the wave Reynolds stress). Considering these shortcomings, a semi-empirical one-dimensional vertical (1DV) model is presented in this study. The present model was obtained using the two-dimensional Navier–Stokes equations and eddy viscosity assumptions, which differ from those of previous researchers, while a top-to-bottom sequence was adopted to calculate the mean current profiles. Empirical formulae were derived from the laboratory measurements and used in the present model to accurately predict the wave boundary layer thickness and bed roughness. The present model is in satisfactory agreement with the data from laboratory experiments. The factors influencing the mean current profiles were analyzed also. The wave-induced second-order shear stresses were found to be the principal reason for the deviations of the mean current profiles in the near-surface layer; as the influencing factors of wave-induced shear stress, the intensity of the wave relative to the current, the angle between the wave and current, and the size of ripples can also have a non-negligible effect on the mean current profiles.

Characteristics of wall-shear stress fluctuations in shock wave and turbulent boundary layer interaction

The wall-shear stress (WSS) fluctuations in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer are investigated by means of direct numerical simulation (DNS) at Mach 2.25. The numerical results agree very well with previous experiments and DNS data in terms of turbulence statistics, wall pressure, and skin friction. The fluctuating WSS characteristics, including probability density function (PDF), frequency spectrum, space–time correlation, and convection velocity, are analysed systematically. It is found that the positively skewed PDF shape of the streamwise WSS fluctuations is significantly changed due to the presence of a separation bubble, while the PDF shape of the spanwise component is slightly affected, exhibiting a symmetric behaviour across the interaction. The weighted power-spectrum density map indicates that the low-frequency unsteadiness associated with the separated shock - exhibits little influence on the spectrum for either component, and no enhancement of the low-frequency energy is observed. A significant reduction in the spatial extent of the two-point correlation is observed, causing spanwise elongated coherence for the streamwise WSS fluctuations in the separation region. Moreover, the elliptic behaviour of the space–time correlations is essentially preserved throughout the interaction, and this is accompanied by a sudden reduction of the convection velocity in the separation bubble.

Bayesian model evaluation of three k–ω turbulence models for hypersonic shock wave–boundary layer interaction flows

Shock wave–boundary layer interaction (SWBLI) is one of the most prevalent challenges in the field of fluid mechanics. Excessive interaction may lead to strong flow separation, which is an important factor causing the deterioration of aircraft performance. Reynolds averaged Navier–Stokes (RANS) models remain the primary methods for predicting flow separation for engineering applications. RANS simulation results typically have uncertainty owing to the drawbacks of the model structure and the variability of the parameters. Therefore, evaluation of a turbulence model based on nominal predictions may be insufficient for reflecting its actual simulation capabilities. In this study, the Bayesian method is employed to re-evaluate the simulation capabilities of three k–ω models for hypersonic SWBLI flows: the original k–ω model and two k–ω models with compressibility corrections (Wilcox's and Zeman's corrections). This is achieved by perturbing the model parameters and combining with experimental data. Bayesian model evaluation based on different datasets is performed using the embedded model error method, and the three turbulence models are compared from three aspects: posterior mean of the quantities of interests, model error, and Bayesian evidence. The results show that the Bayesian calibration can effectively improve the predictive abilities of the three models for wall pressure and wall heat flux. Different from the large differences in the nominal results, the performance of the two calibrated k–ω models with compressibility corrections are very close and superior to that of the original model. Moreover, the evaluation results of this study are also proven to be applicable to other similar flows.

Enhanced atmospheric wave boundary layer model for evaluation of wind stress over waters of finite depth

It is known that the wind stress coefficient on sea surface is a key parameter in modeling ocean waves and depends on the wave condition at the same time, while an ocean wave condition is affected not only by the wind speed over the sea surface but also on the water depth in general. Investigating the effect of water depth on wind stress coefficient is thus of great importance for an accurate wave modeling in shallow waters. In this study, the atmospheric wave boundary layer model is enhanced by considering the effects of water depth on the wind wave spectrum and on the sea spray generation law so that the wind stress can be obtained under more general conditions. In particular, the high-frequency wave spectrum tail is improved by considering the effect of triad wave interaction in shallow waters. A sea spray generation law is developed by including dissipations due to both whitecaps and depth-induced breaking. Numerical results on the wind stress coefficient at different water depth can thus be obtained in good agreement with field observations. A simple formula is also proposed and is applied to modeling hurricane-induced waves on Lake Michigan. The computational results on significant wave heights show that the newly developed method for evaluating wind stress coefficient improves the performance of wave models in finite water depth.

Shock wave and turbulent boundary layer interaction in a double compression ramp

Direct numerical simulations of shock wave and supersonic turbulent boundary layer interaction in a double compression ramp with fixed ramp angles of 12o and 24o at Mach 2.9 are conducted. The characteristics of the shock interactions are investigated for four different length between the two ramp kinks, corresponding to Lc = 0.9δref, 1.8δref, 2.7δref, and 3.6δref (δref being the upstream turbulent boundary layer thickness). The influence of increasing Lc on flow structures, unsteadiness, Reynolds stress, turbulence kinetic energy, and Reynolds stress anisotropy tensor is assessed. The size of the separation region is significantly decreased and reattached flow appears between the two ramp kinks. Streamwise vorticity contours and streamline curvature show the decreased spanwise width and increased spanwise coherency of Görtler-like vortices. Analysis of fluctuating wall pressure indicates that the low-frequency unsteadiness is strongly suppressed in the interaction region. Profiles of Reynolds stress components and turbulence kinetic energy exhibit different turbulence evolution across the interaction, leading to substantial differences observed in the anisotropy invariant map. It is found that the near wall region is characterized by decreased anisotropy, becoming closer to the axisymmetric compression state, while a significant increase of turbulence is identified in the outer region, following the axisymmetric expansion limit. Moreover, downstream of the interaction, turbulence in the near-wall region experiences a faster recovery and the influence of Lc is found to be marginal. The main effect of Lc is observed in the outer region, an increase of Lc resulting in a monotonic decay of turbulence intensities and an inward movement of turbulent structures.

Comment on “The Wave‐Driven Current in Coastal Canopies” by M. Abdolahpour et al.

AbstractLaboratory and field measurements made over the past decade have shown the presence of a strong wave‐driven mean current in submerged vegetation canopies. Luhar et al. (2010, https://doi.org/10.1029/2010jc006345) suggested that this mean current is analogous to the streaming flow generated in wave boundary layers over bare beds, and developed a simple energy and momentum balance model to predict its magnitude. However, this model predicts that the magnitude of the mean current does not depend on canopy spatial density, which is inconsistent with the measurements made by Abdolahpour et al. (2017, https://doi.org/10.1002/2016jc012446) in recent laboratory experiments. Motivated by observations that the wave‐driven mean flow is most pronounced at the canopy interface, Abdolahpour et al. (2017, https://doi.org/10.1002/2016jc012446) proposed an alternate explanation for its origin: It is driven by the vertical heterogeneity in orbital motion created by canopy drag. Such heterogeneity can give rise to incomplete particle orbits near the canopy interface and a Lagrangian mean current analogous to Stokes drift in the direction of wave propagation. A model guided by this physical insight and dimensional analysis is able to generate much more accurate predictions. This comment aims to reconcile these two different models for the wave‐driven mean flow in submerged canopies.

STATISTICAL CHARACTERISTICS OF PRESSURE FLUCTUATION IN SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTION

Shock wave and turbulent boundary layer interaction widely exists in the internal and external flow of high-speed aircraft. The aerodynamic performance and flight safety of aircraft are seriously affected by the strong pressure fluctuation in the interaction region. To investigate statistical characteristics of fluctuating pressure, the interaction between an incident shock of 33.2° and a spatially developed Mach 2.25 turbulent boundary layer is analyzed by means of direct numerical simulation (DNS). The numerical results have been carefully validated against with previous experiment and DNS at similar flow conditions in terms of mean velocity profile, turbulence intensity and wall pressure distribution. Statistics at the wall and in the outer layer, including fluctuation intensity, power spectral density, two-point correlation and space-time correlation, are quantitatively compared. The differences between them are analyzed in detail. It is found that the effect of the shock interaction on the wall-pressure fluctuation and the fluctuating pressure in the outer layer are utterly different. Based on the analysis of the power spectra density, the fluctuations in the separated region are both characterized by the low-frequency content, but in the reattachment region, the peak frequency of outer pressure fluctuations quickly shifts to higher frequency, with the low-frequency energy of wall-pressure fluctuation still being predominant. It is identified that the two-point correlations of pressure fluctuation at the wall and in the outer layer are both more elongated in the spanwise direction than that in the streamwise direction. The integral scale at the wall is generally increased, while the one in the outer layer increases sharply after passing the shock and then gradually decreases. The analysis of space-time correlation indicates that the iso-correlation contours are similar to the elliptical distribution and the convection velocity deduced by the correlation is dramatically decreased. Downstream of the interaction, the convection velocity in the outer layer is higher than that of wall-pressure fluctuation.

Effects of Tip Leakage Flow on the Aerodynamic Performance and Stability of an Axial-Flow Transonic Compressor Stage

To explain the effect of tip leakage flow on the performance of an axial-flow transonic compressor, the compressors with different rotor tip clearances were studied numerically. The results show that as the rotor tip clearance increases, the leakage flow intensity is increased, the shock wave position is moved backward, and the interaction between the tip leakage vortex and shock wave is intensified, while that between the boundary layer and shock wave is weakened. Most of all, the stall mechanisms of the compressors with varying rotor tip clearances are different. The clearance leakage flow is the main cause of the rotating stall under large rotor tip clearance. However, the stall form for the compressor with half of the designed tip clearance is caused by the joint action of the rotor tip stall caused by the leakage flow spillage at the blade leading edge and the whole blade span stall caused by the separation of the boundary layer of the rotor and the stator passage. Within the investigated varied range, when the rotor tip clearance size is half of the design, the compressor performance is improved best, and the peak efficiency and stall margin are increased by 0.2% and 3.5%, respectively.

Influence of viscosity on entropy noise generation through a nozzle

Entropy (temperature) fluctuations produced by turbulent flames generate noise when they are accelerated by the flow. This so-called entropy noise is an important contributor to core noise in modern aeroengines and several semi-analytical models exist in the literature for its prediction. All these models assume the flow to be inviscid. In the present paper, contribution of viscosity on entropy noise generation and scattering through a nozzle is investigated numerically with URANS simulations and analytically through the extension of the 2D inviscid model of Emmanuelli et al. (2020). Simulations indicate noise generation and scattering is slightly reduced in the medium-frequency range in the presence of viscosity with variations below 3 dB in comparison to reference inviscid data. This noise variation is qualitatively well reproduced by the low-order model. The major effect of viscosity on noise generation and propagation lies in the presence of boundary layers. Viscous entropy noise sources and viscous diffusion of acoustic perturbations have a negligible impact on noise. Discrepancies between simulations and analytical solutions are found to come from the radial evolution of the acoustic waves in thick boundary layers, not accounted for in the model, and which impact noise scattering.

Effect of Jet Vortex Generators on Shock Wave Induced Separation on Gas Turbine Profile

The interaction between a shock wave and a boundary layer on a suction side of gas turbine profile, namely Transition Location Effect on Shock Wave Boundary Layer Interaction, was one of main objectives of TFAST project. A generic test section in a transonic wind tunnel was designed to carry out such investigations. The design criteria were to reproduce flow conditions on the profile in wind tunnel as the one existing on the suction side of the turbine guide vane. In this paper, the effect of film cooling and jet vortex generators on the shock wave boundary layer interaction and shock induced separation is presented. Numerical results for Explicit Algebraic Reynolds Stress Model with transition modeling are compared with experimental data.

Analysis and comparison of turbulence model coefficient uncertainty for canonical flow problems

The purpose of this paper is to present results of an uncertainty and sensitivity analysis study of commonly used turbulence models in Reynolds-Averaged Navier–Stokes codes due to the epistemic uncertainty in closure coefficients for a set of turbulence model validation cases that represent the structure of several canonical flow problems. The study focuses on the analysis of a 2D Zero Pressure Gradient Flat Plate, a 2D NASA Wall Mounted Hump, and an Axisymmetric Shock Wave Boundary Layer Interaction, all of which are well documented on the NASA Langley Research Center Turbulence Modeling Resource website. The Spalart–Allmaras (SA), the Wilcox (2006) κ−ω (W2006), and the Menter Shear-Stress Transport (SST) turbulence models are considered in the stochastic analyses of these flow problems, and the FUN3D code was utilized as the flow solver. The uncertainty quantification approach involves stochastic expansions based on non-intrusive polynomial chaos to efficiently propagate the uncertainty. Sensitivity analysis is performed with Sobol indices to rank the relative contribution of each closure coefficient to the total uncertainty for several output flow quantities. The results generalize a set of closure coefficients which have been identified as contributing most to the uncertainty in various output quantities of interest for the set of canonical flow problems considered in this study. Mainly, the SA turbulence model is most sensitive to the uncertainties in the diffusion constant (σ), the log layer calibration constant (κ), and the turbulent destruction constant (cw2). The predictive capability of the W2006 model is most sensitive to the uncertainties in a dissipation rate constant (σw), the shear stress limiter (Clim), and a turbulence-kinetic energy constant (β*). Likewise, the SST turbulence model was found to be most sensitive to the diffusion constants (σw1 and σw2), the log layer calibration constant (κ), and the shear stress limiter (a1).