Production Of Turbulent Kinetic Energy Research Articles

Investigation on the turbulent structures in combined wave-current boundary layers

The problem of turbulent vortices and vortex dynamics under the influence of ocean waves is a subject of continuing research in the field of wave-current interaction. Thus, this study investigates the evolution of turbulence structures and vortex interactions in combined wave-current boundary layers, where water waves propagate with currents. Experiments were performed in two glass-walled laboratory channels with water depths of 160 and 400 mm. A two-dimensional two-component (2D2C) Particle Image Velocimetry (PIV) system was used to measure the velocities. Periodic variations in turbulence are observed for combined wave-current flows. Pairs of counter-rotating vortices are identified in the outer region when the combined flow is reversed, leading to destructive vortex interactions. This process leads to a reduction in the turbulent kinetic energy (TKE) and TKE production and dissipation during the passage of the wave trough. A conceptual model of hairpin vortices in combined wave-current flows is proposed in this study. The results of this study provide novel insights into the hydrodynamics of combined wave-current flows.

A modification of production term for the shear stress transport turbulence model based on a new wall-law for adverse pressure gradient

This paper presents an attempt to improve the predictive accuracy of the Menter shear stress transport (SST) turbulence model for adverse pressure gradient (APG) flows. The foundation of this work lies in the newly modified law of the wall and turbulent kinetic energy (TKE) transport equation within the APG turbulent boundary layer. The modification of the law of the wall is achieved through a newly proposed variable λ, which is derived theoretically and calibrated using direct numerical simulation data. Based on the new law of the wall, we analyze the TKE transport equation of the SST model at APG and demonstrate that the analytical solution satisfying the law of the wall cannot achieve equilibrium in the current SST model. Further theoretical analysis reveals that this imbalance is caused by the TKE production term Pk, and the decomposition of the wall friction coefficient Cf indicates that Pk directly affects the prediction of flow separation. Based on the analysis and the new law of the wall, an additional term for Pk is suggested to correct Pk and improve the model's predictive accuracy for APG flows. Numerical validation results show that the correction leads to an increase in Pk within the APG turbulent boundary layer, resulting in more accurate predictions of Cf and the mean velocity profile in the inner layer of the turbulent boundary layer.

Spacing Ratio Effects on the Evolution of the Flow Structure of Two Tandem Circular Cylinders in Proximity to a Wall

The flow around two tandem circular cylinders in proximity to a wall is investigated using particle image velocimetry (PIV) for Re = 2 × 103. The spacing ratios L/D are 1, 2, and 5, and the gap ratios G/D are 0.3, 0.6, and 1. The proper orthogonal decomposition (POD) method and λci vortex identification method are used to investigate the evolution of flow structure, and the influences of L/D and G/D on flow physics are shown. At L/D = 2 and G/D = 0.3, a “pairing” process occurs between the wall shear layer and the upstream cylinder’s lower shear layer, resulting in a small separation bubble behind the upstream cylinder. At L/D = 1, the Strouhal number (St) increases with decreasing G/D. At three gap ratios, the St gradually decreases as L/D increases. At G/D = 0.3, there is nearly a 49.98% decrease from St = 0.3295 at L/D = 1 to St = 0.1648 at L/D = 5, which is larger than the reductions in cases of G/D = 0.6 and G/D = 1. The effects of L/D on the evolution of flow structure at G/D = 0.6 are revealed in detail. At L/D = 1, the vortex shedding resembles that of the single cylinder. As L/D increases to 2, a squarish flow structure is formed between two cylinders, and a small secondary vortex is formed due to induction of the lower shear layer of the upstream cylinder. At L/D = 5, there is a vortex merging process between the upper wake vortices of the upstream and downstream cylinders, and the lower wake vortex of the upstream cylinder directly impinges the downstream cylinder. In addition, the shear layers and wake vortices of the upstream cylinder interact with the wake of the downstream cylinder as L/D increases, resulting in reductions in velocity fluctuations, and the production and turbulent diffusion of turbulent kinetic energy are decreased behind the downstream cylinder.

Reynolds number effect on the parameters of turbulent flows over open channels

Abstract Experimental investigations were conducted to analyze the effect of Reynolds numbers on turbulent flow properties in a nonuniform sand bed channel. Steady flow simulations were performed over the nonuniform sand bed channel, considering five Reynolds numbers within the range of 36500–53886. This article endeavors to delineate the influence of Reynolds number on turbulent flow properties through meticulous laboratory studies. Observations revealed that higher Reynolds numbers corresponded to increased longitudinal velocity. As the Reynolds number increases by 10 to 47%, various turbulent flow properties exhibit distinct trends. Specifically, the longitudinal velocity, longitudinal turbulent intensity, vertical turbulent intensity, turbulent kinetic energy, Reynolds shear stress, and Taylor scale show increases ranging from 5 to 30%, 15 to 25%, 15 to 20%, 25 to 60%, 20 to 40%, and 35 to 45%, respectively. Taylor scale analysis indicated higher magnitudes associated with higher Reynolds numbers. In-depth examinations of turbulent anisotropy, third-order moments of velocity fluctuations, kurtosis, turbulent kinetic energy production, and dissipation provided additional insights into flow behavior across different Reynolds numbers. This study contributes to a more comprehensive understanding of flow dynamics in nonuniform sand bed channels under varying Reynolds number conditions, bridging the gap between laboratory studies and real-world scenarios.

Experimental assessment of square-wave spatial spanwise forcing of a turbulent boundary layer

We present an experimental realisation of spatial spanwise forcing in a turbulent boundary layer flow, aimed at reducing the frictional drag. The forcing is achieved by a series of spanwise running belts, running in alternating spanwise direction, thereby generating a steady spatial square-wave forcing. Stereoscopic particle image velocimetry in the streamwise–wall-normal plane is used to investigate the impact of actuation on the flow in terms of turbulence statistics, drag performance characteristics, and spanwise velocity profiles, for a non-dimensional wavelength of λx+=397\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda _x^+ = 397$$\\end{document}. In line with reported numerical studies, we confirm that a significant flow control effect can be realised with this type of forcing. The scalar fields of the higher-order turbulence statistics show a strong attenuation of stresses and production of turbulence kinetic energy over the first belt already, followed by a more gradual decrease to a steady-state energy response over the second belt. The streamwise velocity in the near-wall region is reduced, indicative of a drag-reduced flow state. The profiles of the higher-order turbulence statistics are attenuated up to a wall-normal height of y+≈100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y^+ \\approx 100$$\\end{document}, with a maximum streamwise stress reduction of 45% and a reduction of integral turbulence kinetic energy production of 39%, for a non-dimensional actuation amplitude of A+=12.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A^+ = 12.7$$\\end{document}. An extension of the classical laminar Stokes layer theory is introduced, based on the linear superposition of Fourier modes, to describe the non-sinusoidal boundary condition that corresponds to the current case. The experimentally obtained spanwise velocity profiles show good agreement with this extended theoretical model. The drag reduction was estimated from a linear fit in the viscous sublayer in the range 2≤y+≤5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2 \\le y^+\\le 5$$\\end{document}. The results are found to be in good qualitative agreement with the numerical implementations of Viotti et al. (Phys Fluids 21, 2009), matching the drag reduction trend with A+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A^+$$\\end{document}, and reaching a maximum of 20%.Graphical abstract

Tracking the Nearfield Evolution of an Initially Shallow, Neutrally Buoyant Plane Jet Over a Sloping Bottom Boundary

AbstractUnderstanding coastal plane jets which occur when a body of water discharges into an ocean or a lake through a channel or outlet is important, since they play a significant role in sediment, nutrient, and pollutant exchange. This study investigates the nearfield of initially shallow, neutrally buoyant plane jets, bounded by a free surface and a sloping bottom (Sloping Bottom Jet; SBJ) that issue into a laterally unconfined quiescent ambient both experimentally and numerically, and compares them with a plane jet flowing over a horizontal bottom (Horizontal Bottom Jet; HBJ). Results revealed that, different from the HBJ, the width and centerline velocity of SBJ decrease near the mouth. The SBJ width gradually increases after that as the transverse longitudinal velocity profile progressively transforms from a “top‐hat” into a Gaussian distribution. Once the Gaussian distribution is established, both jets diverge and centerline velocity decreases. Shear layers are generated on the sides of both jets with Kelvin Helmholtz‐type Coherent Structures (KHCS) developing inside. KHCS produce periodic velocity fluctuations with a Strouhal number of ∼0.079 and contribute significantly to momentum exchange and turbulent kinetic energy production. Since the thickness of the SBJ increases longitudinally, the vertical extent of KHCS also increases. When the two shear layers meet and merge at the centerline, they cause a flapping motion of the jet. This location is closer to the jet mouth for SBJs than for the HBJ. These findings demonstrate that a sloping bottom modifies the flow field from quasi‐2D for the HBJ to strongly 3D for SBJs.

Assessment of Laws of the Wall During Flame–Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

The validity of the usual laws of the wall for Favre mean values of the streamwise velocity component and temperature for non-reacting flows has been assessed for turbulent premixed flame-wall interaction using Direct Numerical Simulation (DNS) data. Two different DNS databases corresponding to friction velocity-based Reynolds number of 110 and 180 representing unsteady head-on quenching of statistically planar flames within turbulent boundary layers have been considered. The usual log-law based expressions for the Favre mean values of the streamwise velocity and temperature for the inertial layer have been found to be inadequate at capturing the corresponding variations obtained from DNS data. The underlying assumptions of constant shear stress and the equilibrium of production and dissipation of turbulent kinetic energy underpinning the derivation of the usual log-law for the mean streamwise velocity have been found to be rendered invalid within the usual inertial layer during flame-wall interaction for both cases considered here. The heat flux does not remain constant within the usual inertial layer, and the turbulent flux of temperature exhibits counter-gradient transport within the so-called inertial layer for the cases considered in this work. These render the assumptions behind the derivation of the usual log-law for temperature to be invalid for application to turbulent flame-wall interaction. It has been found that previously proposed empirical modifications to the existing laws of the wall, which account for density and kinematic viscosity variations with temperature, do not significantly improve the agreement with the corresponding DNS data in the inertial layer and the inaccurate approximations for the kinematic viscosity compensated wall normal distance and the density compensated streamwise velocity component contribute to this disagreement. The DNS data has been utilised here to propose new expressions for the kinematic viscosity compensated wall normal distance and the density compensated streamwise velocity component, which upon using in the empirically modified law of wall expressions have been demonstrated to provide reasonable agreement with DNS data.

Direct numerical simulations of supersonic flat-plate turbulent boundary layers with uniform blowing

The effect of uniform blowing on a spatially developing flat-plate turbulent boundary layer at Mach 2.25 is investigated using direct numerical simulations. Two values of the wall blowing ratio are considered, corresponding to low and high blowing rates. Uniform blowing is found to significantly reduce the near-wall turbulence anisotropy, although the turbulent kinetic energy still exhibits near-wall asymptotic behavior and the Reynolds analogy is relatively insensitive to changes in the blowing ratio. The pre-multiplied spectra of turbulent kinetic energy production demonstrate that increasing the blowing ratio significantly energizes the large-scale structures in the outer region, while suppressing the inner small-scale structures. An increase in the blowing ratio also has a strong influence on the behavior of the fluctuating wall pressure, amplifying the fluctuation intensity and reducing the dominant frequencies in the power spectrum. Two-point space–time correlations indicate that the characteristic length scale of the pressure fluctuations increases with increasing blowing ratio, whereas the convection velocity exhibits the opposite trend. Analysis of the reduced mean wall heat flux reveals that it is dominated by the relative balance between the work of the Reynolds stress and the turbulent transport of heat, but is insensitive to uniform blowing. Importantly, bidimensional empirical mode decomposition of the turbulent structures highlights the increasingly dominant contributions related to the significantly energized outer large-scale structures in the blowing region.

Direct numerical simulations of high-enthalpy supersonic turbulent channel flows including finite-rate reactions

Direct numerical simulations of temporally evolving high-enthalpy supersonic turbulent channel flows are conducted at a Mach number of 3.0 and Reynolds number of 4880 under isothermal wall conditions. Air is assumed to behave as a five-species mixture, and chemical non-equilibrium and equilibrium assumptions are adopted to investigate the influence of finite-rate reactions on the turbulent statistics and large-scale structures. The two wall temperatures of 1733.2 and 3500 K are such that the mixture components undergo strong dissociation and recombination reactions along the channel. Investigation shows that the turbulent intensity is weakened and the mean and fluctuating temperatures are smaller when finite-rate reactions are considered. The mean dissociation degree is a quadratic function of the normal position, and its curvature under the chemical non-equilibrium assumption is greater than that under the chemical equilibrium assumption. The fluctuating mass fractions of the generated species seem to decrease slightly in the near-wall region, and their distributions are obviously different from those of the fluctuating velocity and fluctuating temperature. Finite-rate reactions increase the proportion of turbulent kinetic energy production in the skin friction decomposition, especially when the wall temperature is 3500 K. The large-scale structures visualized by the cross correlation between temperature and species mass fraction become stronger in the normal direction. The turbulent Schmidt number and several velocity–temperature correlations, including the recovery enthalpy and strong Reynolds analogy, are insensitive to the chemical reaction rate and wall temperature.

Free convection in a differentially heated square cavity filled with low-Prandtl-number materials: Numerical studies using transition shear stress transport model

Computing the flow field under free convection in a cavity becomes particularly challenging for low-Prandtl-number (Pr) fluids typically encountered for liquid metals. The objective of the present study is to investigate the natural convection process in a differentially heated square cavity employing the transition shear stress transport (SST) model for the Prandtl number Pr∈[0.001,0.1] and the Rayleigh number Ra∈[104,1010]. The mean flow field is visualized through streamlines, isotherms, non-dimensional velocity, and temperature profiles, turbulence intensity, contours of intermittency (γ) times, the production of turbulent kinetic energy (Pκ), and distribution of skin friction coefficient and the Nusselt number (Nu). The transition SST model can capture the mean flow field and thermal transport over the entire parametric regime successfully. An average Nusselt number (Nu¯) on the hot wall is found to scale with a certain power (n) of the Boussinesq number (Bo), the product of Ra and Pr. The value of n is 0.18 for Ra up to 106 and 0.25 for higher Ra.

Flow analysis through a randomly packed pebble-bed geometry using computational fluid dynamics

This study presents a comprehensive analysis of the flow behavior in packed pebble-bed reactors using computational fluid dynamics (CFD) simulations. The pebble-bed geometry corresponds to an experimental facility located at the Texas A&M Thermal-Hydraulics Research Laboratory. The unsteady Reynolds-averaged Navier–Stokes (URANS) k−ω shear stress transport (SST) and the large eddy simulation (LES) approaches were selected to model the turbulence at different Reynolds numbers. The numerical models were first validated by comparing the pressure drop results obtained from the simulations against established correlations, finding the simulation predictions in accurate agreement. Secondly, the velocity first-order statistics from the URANS k−ω SST and LES calculations were also contrasted with the available experimental particle image velocimetry data to validate the numerical models. Results were found in reasonable agreement as the mean absolute error achieved values smaller than 10% of the inlet velocity for most of the analyzed velocity profiles. A comprehensive turbulence characterization was performed, including second-order statistics, Reynolds stress anisotropy, and turbulent kinetic energy production. The proper orthogonal decomposition of the fluctuating velocity was examined in the current flow domain. The turbulence characterization revealed the complex nature of turbulence in packed pebble-bed geometries, which is further complicated by the presence of an enclosing wall. Overall, the findings of this study provide a solid foundation for the development of more accurate CFD-based methodologies for predicting the behavior of flow through packed pebble-bed reactors.

Impact of Momentum Perturbation on Convective Boundary Layer Turbulence

AbstractMesoscale‐to‐microscale coupling is an important tool for conducting turbulence‐resolving multiscale simulations of realistic atmospheric flows, which are crucial for applications ranging from wind energy to wildfire spread studies. Different techniques are used to facilitate the development of realistic turbulence in the large‐eddy simulation (LES) domain while minimizing computational cost. Here, we explore the impact of a simple and computationally efficient Stochastic Cell Perturbation method using momentum perturbation (SCPM‐M) to accelerate turbulence generation in boundary‐coupled LES simulations using the Weather Research and Forecasting model. We simulate a convective boundary layer (CBL) to characterize the production and dissipation of turbulent kinetic energy (TKE) and the variation of TKE budget terms. Furthermore, we evaluate the impact of applying momentum perturbations of three magnitudes below, up to, and above the CBL on the TKE budget terms. Momentum perturbations greatly reduce the fetch associated with turbulence generation. When applied to half the vertical extent of the boundary layer, momentum perturbations produce an adequate amount of turbulence. However, when applied above the CBL, additional structures are generated at the top of the CBL, near the inversion layer. The magnitudes of the TKE budgets produced by SCPM‐M when applied at varying heights and with different perturbation amplitudes are always higher near the surface and inversion layer than those produced by No‐SCPM, as are their contributions to the TKE. This study provides a better understanding of how SCPM‐M reduces computational costs and how different budget terms contribute to TKE in a boundary‐coupled LES simulation.

Vortex ring breakdown dominating the entrainment of a synthetic jet

The understanding of the entrainment mechanism of synthetic jets can help optimise the synthetic jet actuators in engineering applications. It is generally believed that vortex rings or strong velocity fluctuations in the near field of the synthetic jet are responsible for its enhanced entrainment. However, in recent years, it has been found that the enhanced entrainment of the synthetic jet may be caused by the instability or the vortex ring breakdown in the transition region. To shed new light on this issue, synthetic jets with different Reynolds numbers and dimensionless stroke lengths are investigated with time-resolved two-dimensional particle image velocimetry. Based on the analyses of velocity triple-decomposition, Fourier mode decomposition and phase-averaged $\lambda _{ci}D/U_0$ field, the streamwise positions of the vortex ring breakdown are determined for the synthetic jets, and the entrainment coefficient can be divided into three components, i.e. the coherent turbulent kinetic energy production, the random turbulent kinetic energy production and the shape of the velocity profile. It is found that the entrainment coefficient is dominated by the component related to the random turbulent kinetic energy production, and reaches its peak value at the position of vortex ring breakdown. The results obtained in different cases show a strong correlation between vortex ring breakdown and entrainment enhancement. From the perspective of instantaneous snapshot, the mechanism of vortex ring breakdown enhanced entrainment is revealed, that is, vortex ring breakdown enhanced the small-scale vortex near the turbulent/non-turbulent interface, resulting in an increase of enstrophy production, and thus enhanced local entrainment.

A generalized slab model

Abstract We construct a generalized slab model to calculate the ocean’s linear response to an arbitrary, depth-variable forcing stress profile. To introduce a first-order improvement to the linear stress profile of the traditional slab model, a nonlinear stress profile which allows momentum to penetrate into the transition layer (TL) is used (denoted ‘mixed layer/transition layer,’ or MLTL stress profile). The MLTL stress profile induces a two-fold reduction in power input to inertial motions relative to the traditional slab approximation. The primary reduction arises as the TL allows momentum to be deposited over a greater depth range, reducing surface currents. The secondary reduction results from the production of turbulent kinetic energy (TKE) beneath the mixed layer (ML) related to interactions between shear stress and velocity shear. Direct comparison between observations in the Iceland Basin, the traditional slab model, the generalized slab model with the MLTL stress profile, and the Price-Weller-Pinkel (PWP) model suggest that the generalized slab model offers improved performance over a traditional slab model. In the Iceland Basin, modeled TKE production in the TL is consistent with observations of turbulent dissipation. Extension to global results via analysis of Argo profiling float data suggests that on the global, annual-mean, ∼ 30% of the total power input to near-inertial motions is allocated to TKE production. We apply this result to the latest global, annual-mean estimates for near-inertial power input (0.27 TW) to estimate that 0.08 ± 0.01 TW of the total near-inertial power input are diverted to TKE production.

Impact of urban land use on mean and heavy rainfall during the Indian summer monsoon

Abstract. Northern India has undergone intense urbanization since the middle of the 20th century. The impact of such drastic land-use change on the regional weather and climate remains to be assessed. In this work, we study the impact of the modification of land use – from vegetation to urban – on the Indian summer monsoon rainfall as well as on other meteorological variables. We use the regional Meso-scale Non-Hydrostatic (Meso-NH) model coupled with an urban module (the Town Energy Balance model) to perform monthlong sensitivity simulations centered around Kolkata, the most urbanized area in northeastern India. Paired simulations, one with and another without urban settings, have been performed to identify the impacts related to urbanization through both thermodynamic and kinetic effects. We find that the perturbation induced by urban land use enhances the mean rainfall over the model domain, principally by intensifying the convective activity through thermodynamic perturbation, leading to a 14.4 % increase in the monthly mean rainfall. The urban area also induces a 15.0 % rainfall increase during two modeled periods of heavy precipitation caused by low-pressure systems. In addition, the modeling results demonstrate that the urban area not only generally acts as a rainfall enhancer, particularly during nighttime, but also induces the generation of a specific storm in one modeled case that would not have formed in the absence of the urban area. The initiation of this storm over the city was primarily due to the urban terrain's disturbance of the near-surface wind flow, leading to a surge in dynamically produced turbulent kinetic energy (TKE). The thermal production of TKE over the nighttime urban boundary layer, on the other hand, serves as a contributing factor to the storm formation.

Effect of hemispherical roughness spacing on double-averaged turbulence characteristics for different flow submergence

The double-averaged (DA) turbulence characteristics over rough bed comprising of hemispherical elements with different spacing ( p/ r = 2, 4, 6, and 8; p = pitch distance; r = height of hemisphere) is quantified for three flow-submergences ( h/ r = 7.14, 5.35, 3.57; mean flow-depth ( h) = 20 cm, 15 cm, and 10 cm). The production and dissipation rates of turbulent kinetic energy are maximum at and below the crest level. Within interfacial sublayer, the degree of anisotropy is observed to be maximum for p/ r = 4 and the tendency for the return to isotropy is strongest for p/ r = 8 in the outer layer. The turbulence generated in the bottom region is still present in the outer region for low flow-submergences. The turbulence strength is maintained in the roughness order (descending) as p/ r = 4 > 2 > 6 > 8 > plane bed; wherein the change in flow-submergence does not change this order.

Direct numerical simulation of turbulence amplification in a strong shock-wave/turbulent boundary layer interaction

In this study, the turbulence amplification mechanism within the strong shock-wave/turbulent boundary layer interaction is investigated using direct numerical simulation (DNS) over a 24° compression ramp with Mach 2.9 flow. A new in-house solver based on the compact finite difference scheme is introduced, and its accuracy is validated by comparing the flow statistics with existing DNS and experimental data. Within the DNS findings, two distinct turbulence kinetic energy (TKE) hotspots are identified. In contrast to previous studies, this study sheds light on shocklets, characterized by mid-frequency features, as a key factor contributing to the second TKE amplification, which occurs near the reattachment point. Streamline coordinate analysis reveals that shear effects dominate TKE production over the flow deceleration effect in the shock-wave/turbulent boundary layer interaction. The shear effect induced by the rolling up of the boundary layer initiates the first TKE amplification near the wall region in proximity to the separation point, followed by flow deceleration due to the main shock wave contributing to TKE generation. The initial detachment of the shear layer enhances the shear contribution. While TKE decreases above the separation bubble due to the positive mean velocity gradient, TKE amplifies again due to the flow deceleration caused by the secondary shock wave. In addition, the intermittently spawning shocklets above the bulge structures enhance the shear effect on the TKE production. Moreover, the generated TKE subsequently transfers to the local pressure minimum line, created by the bulges effect, thereby establishing a spatially converged maximum TKE line.

Direct Numerical Simulation of High-Enthalpy Turbulent Boundary-Layer Flow with Light Gas Injections

Two light gases (He and H2) are, respectively, introduced upstream of a high-enthalpy turbulent flat-plate flow with a boundary-layer edge Mach number of Maδ=2.25 and temperature of Tδ=1800  K. The flow condition refers to the after-shock wave flow on a blunt-body hypersonic vehicle (Duan and Martín, AIAA Journal, Vol. 49, No. 1, 2011, pp. 172–184). Direct numerical simulation results show that the injection of these light gases has little effect on the mean velocity profiles but significantly reduces the near-wall density and skin friction. The separation and fragmentation of near-wall vortical structures are restrained, and the Reynolds shear stress decreases. The injection of inert He inhibits the dissociation reaction of O2 and weakens the chemical nonequilibrium effect, resulting in enhanced mean and fluctuating temperatures. The injection of active H2 promotes the reaction between H2 and O2, which increases the mean temperature but inhibits its fluctuation. After decomposing the mean skin friction into physics-informed contributions, both injections largely reduce the turbulent kinetic energy production term Cf,T and the spatial growth term of the flow, Cf,G, through lowering the near-wall density and reducing vortices.

Interrelationships of entropy production and turbulence kinetic energy associated with simple angle and compound angle full coverage film cooling

The present paper compares experimentally-measured distributions of entropy generation with numerically-predicted distributions of streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy. These comparisons are provided for two full-coverage film cooling environments which are designed to model the thermal management arrangements employed for combustor liners within gas turbine engines. One of these arrangements includes alternating compound angle values of +30° in one row of holes, followed by −30° in the next row of holes. The other arrangement includes simple angle holes with a zero degree compound angle value. The associated full-coverage film cooled boundary layers are investigated within a double-wall cooling test facility wherein the air for each full-coverage film cooling arrangement is provided by an impingement jet array. Experimentally-measured entropy generation values are obtained from film cooled boundary layer measurements of local total pressure variations, obtained in isothermal flow, relative to the freestream values outside of the boundary layer. The resulting entropy generation values quantify second law losses, which are associated with aerodynamic gains. To obtain the associated numerical-prediction results for a steady-state, three-dimensional flow field, employed is the ANSYS FLUENT Version 2022 R2 computational code with a SST k–ω turbulence closure model. The resulting comparisons of entropy generation, streamwise vorticity, turbulence kinetic energy, and production of turbulence kinetic energy are provided for a blowing ratio BR of 2.9 for simple angle film cooling with a main flow Reynolds number Rems of 138,000, and for compound angle film cooling with a main flow Reynolds number Rems of 142,000. Overall, evidence is provided of strong relationships between local turbulence kinetic energy and local entropy production since the two quantities are highly correlated with each other over s substantial range of experimental conditions and configurations. For example, ratio of turbulence kinetic energy to entropy generation data collapse for Z/de values from 0 to 3.5 for Y/de = 0.5, Y/de = 1.5, and both film cooling arrangements. Here, the value of the TKE/Sgen ratio is approximately constant for these conditions, which evidences direct and simple dependences of local turbulence kinetic energy upon local entropy generation, even for lower magnitudes of Z/de. The direct and simple dependences of local turbulence kinetic energy upon local entropy generation are further illustrated by the simplicity of linear correlation equations, which represent physical behavior for different conditions and configurations. These correlation equations are developed for three arrangements, which are associated with X/de = 54.54.

Turbulent transport mechanism in the roughness sublayers over idealized urban areas and its implication to street-level ventilation

Turbulence in the roughness sublayer (RSL) is inhomogeneous compared with that in the inertial sublayer (ISL) of the atmospheric surface layer (ASL) over urban areas. Drag coefficient Cd, which measures aerodynamic roughness, is employed in this paper to examine how (idealized) urban morphology influences ASL dynamics and transport. Wind tunnel experiments are conducted to study the flows and turbulence in response to different configurations of (identical) roughness elements. Statistics, quadrant analysis, and tilt angle evidence the more efficient RSL transport over rougher surfaces even the winds are slower. Although the power spectra of streamwise u’’ and vertical w’’ fluctuating velocities are rather insensitive to Cd, their cospectrum shows a secondary peak at small motion scales λx (≤ 0.1δ where δ is the thickness of turbulent boundary layer) along with the primary peak at integral length scale Λx (≈ δ). It is thus suggested that, regardless of the turbulence intensity, RSL streamwise and vertical winds are more correlated, enhancing the transport. Amplitude (AM) and frequency (FM) modulations signify the positive correlation between RSL large and small motion scales which is amplified over rougher surfaces. Furthermore, RSL turbulence kinetic energy (TKE) production (entrainment) increases with decreasing (increasing) Cd, fostering the basic mechanism of street-level ventilation.