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It is well known that low- and high-speed velocity streaks are statistically asymmetric. However, it is unclear how different the low- and high-temperature structures (T-structures) are even though they are strongly coupled with the streamwise velocity. Therefore, this paper identifies three-dimensional wall-attached temperature structures in supersonic turbulent boundary layers over cooled and heated walls (coming from direct numerical simulations) and separates them into positive and negative families. Wall-attached T-structures are self-similar; especially, the length and width of the positive family are linear functions of the height. The superposed temperature variance in both positive and negative families exhibits a logarithmic decay with the wall distance, while the superposed intensity of the wall-normal heat flux in the negative family shows a logarithmic growth. The modified strong Reynolds analogy proposed by Huang, Coleman, and Bradshaw ["Compressible turbulent channel flows: DNS results and modelling," J. Fluid Mech. 305, 185–218 (1995)] is still valid in the negative family. The relative position between T-structures of opposite signs depends on the wall temperature and that in the cooled-wall case differs significantly from the relative position between low- and high-speed streaks, especially those tall ones. In the cooled-wall case, although positive temperature fluctuations below and above the maximum of the mean temperature can cluster to large-scale wall-attached structures, they are very likely dynamically unrelated. [ABSTRACT FROM AUTHOR]

The characteristics of wall heat flux (WHF) beneath a supersonic turbulent boundary layer interacting with an impinging shock wave with a 33.2° angle at Mach 2.25 are analyzed using direct numerical simulation. It is found that the QP85 scaling, defined as the ratio of the mean WHF and wall pressure, changes across the interaction. The probability density function of the WHF fluctuations normalized by the local root-mean-squared value is similar to that of wall shear stress. Comparing the WHF and wall pressure spectra shows that the low-frequency shock unsteadiness exhibits little influence on the spectrum. The space–time correlation of the fluctuating WHF reveals that both the streamwise correlation length scale and the convection velocity experience a sharp decrease in the separation region and subsequent recovery in the downstream region. Moreover, the mean WHF in an incident shock interaction is decomposed for the first time. An analysis of the velocity and temperature fluctuations based on bidimensional empirical mode decomposition is performed to evaluate the contribution of turbulent structures with specific spanwise length scales to the mean WHF generation. The decomposed results indicate that the contribution associated with the large-scale structures in the outer region is greatly amplified by the shock interaction and has the leading role in the generation downstream of the interaction. [ABSTRACT FROM AUTHOR]

In the present study, we perform direct numerical simulations to study the influences of the spanwise-oriented grooves, which are emulated by the reasonably designed "relaxed" boundary conditions, on the kinetic and thermodynamic statistics in a supersonic turbulent channel flow at the Mach number of 1.5 and Reynolds number of 3000. The phase averaged flow fields show that the relaxed boundary induces compressive and expansive waves that travel across the whole channel and are reflected by the upper wall. These waves are isentropic in the average sense except in the viscous sublayer. In the near-wall region, vortices and streaks that constitute the self-sustaining cycles are less populated and less meandering, while in the outer region, especially near the channel center, the velocity divergence is as strong as the vorticity. The temperature, density, and pressure fluctuations are enhanced by these waves. The correlations between the velocity and temperature are altered, due to the counter effects caused by the vortical motions and isentropic waves. [ABSTRACT FROM AUTHOR]

To understand fundamental problems in hypersonic laminar-turbulent boundary layer transition for three-dimensional complex vehicles, a new standard model with typical lifting-body features has been proposed, named as hypersonic transition research vehicle (HyTRV). The configuration of HyTRV is fully analytical, and details of the design process are discussed in this study. The transition characteristics for HyTRV are investigated using three combined methods, i.e., theoretical analyses, numerical simulations, and wind tunnel experiments. Results show that the fully analytic parameterization design of HyTRV can satisfy the model simplification requirements from both numerical simulations and wind tunnel experiments. Meanwhile, the flow field of HyTRV reveals typical transition mechanisms in six relatively separated regions, including the streamwise vortex instability, crossflow instability, secondary instability, and attachment-line instability. Therefore, the proposed HyTRV model is valuable for fundamental researches in hypersonic boundary layer transition. A new standard model with typical lifting-body features for boundary layer transition research has been proposed. Results of three combined analysis methods show that the flow field of HyTRV reveals typical transition mechanisms in six relatively separated regions, including the streamwise vortex instability, crossflow instability, secondary instability, attachment-line instability. Therefore, the proposed HyTRV model is valuable for fundamental researches in hypersonic boundary layer transition. [ABSTRACT FROM AUTHOR]

Since projectiles with large slenderness ratio are prone to elastic deformation, the effect of structural deformation is necessary to be taken into consideration for dynamic modeling. In order to obtain the precise aerodynamic performance and flight dynamic characteristics of flexible projectiles, a new numerical flight simulation system is developed based on computational fluid dynamics and generalized dynamic-mesh technique. Furthermore, flight dynamic stability of a typical flexible projectile is carried out in detail by introducing PID controller. By means of installing the sensors at various locations, the effect of different mode shapes on the characteristics of the closed-loop flight dynamic system is researched. Numerical results indicate that, when the disturbance due to elastic vibration is added into the mixed signals gained from the angular velocity/acceleration sensors, the feedback response of the closed-loop system becomes adversely divergent. In contrast, the stability of the closed-loop system is not sensitive to the elastic disturbance added to the centroid velocity and acceleration. Moreover, the stability of closed-loop system is much less affected by the unsteady aerodynamic loading due to elastic vibration than the interference of the elastic vibration on the dynamic signals detected by the sensors. The phenomenon can be explained by the requirement on the stability of the long and short period modes of flight dynamics, which can provide some guidance for the layout of the sensor and the design of control system of the projectiles with large slenderness ratio. [ABSTRACT FROM AUTHOR]

We perform direct numerical simulations to investigate the characteristics of wall heat flux (WHF) in the interaction of an oblique shock wave at an angle of 33.2° and free-stream Mach number M∞ = 2.25 impinging on supersonic turbulent expansion corners with deflection angles of 0o (flat plate), 6o and 12o. The effect of the expansion on the WHF characteristics is analysed by comparing it to the interaction with the flat plate under the same flow conditions and a fixed shock impingement point. In the post-expansion region, the decreased mean WHF is found to collapse onto the flat plate case when scaled with the mean wall pressure. The statistical properties of the WHF fluctuations, including probability density function, frequency spectra, and space–time correlations, are comparatively analysed. The expansion causes an increase in the occurrence probability of negative extreme events, an enhancement of high-frequency energy, and an inhibition of intermediate-frequency energy. The increased expansion angle also results in a faster recovery of characteristic spanwise length scales and an increase in convection velocity. We use the mean WHF decomposition method in conjunction with bidimensional empirical mode decomposition to quantitatively analyse the impact of expansion on scale contributions. It is demonstrated that the presence of the expansion corner has no significant impact on the decomposed results, but it significantly reduces the contribution associated with outer large-scale structures. [ABSTRACT FROM AUTHOR]

In this work, we carry out direct numerical simulations of particle suspensions in the compressible turbulent vertical channel (TVC) flows with Mach number Ma = 1.5 and particle Stokes number St = 1–100. The compressibility effect is considered in the particle dynamic model for the first time in the study of compressible particle-laden wall turbulence. We find that in both incompressible and compressible flow, gravity weakens the wall-normal and spanwise fluctuations of particle velocities as the Stokes number increases. However, compared to the incompressible flow case, the compressible effect amplifies the mean velocity, fluctuations of velocity, and slip velocity of particle in the streamwise direction. The wall-normal and spanwise fluctuations of particle velocities are augmented by the compressible effect in the channel core region. Moreover, in the core region, the effect of fluid compressibility on the wall-normal and spanwise fluctuations of particle velocities attenuates as the Stokes number increases, indicating a competition between the compressible effect and the particle inertia effect. We, furthermore, conduct the quadrant analysis of the local fluctuation velocities of fluid at particle positions and observe preferential distributions in the second and the fourth quadrants at y+ = 12.5–13.5. For compressible TVC flows, the pattern of probability distributions is more elongated, and the percentage is slightly higher in the second and fourth quadrants than that of incompressible flows. This observation implies that more particles locate in the ejection and sweep events in compressible flows than that in incompressible flows, which is anticipated to influence the particle wall-normal transport. [ABSTRACT FROM AUTHOR]

To study the problem about dynamic destabilization of the reentry vehicles, the bifurcation theory of nonlinear autonomous dynamic system is used together with the unsteady Navier-Stokes equations simulating the pitching process. The investigations shown th at, the astronautic vehicles reentering into the atmosphere would generally occur a dynamic destabilization of pitching motion as their flight Mach number decreased, and the phenomenon of dynamic destabilization befallens at the point of the Hopf bifurcation, furthermore, there are two types of Hopf bifurcation named subcritical Hopf bifurcation and supercritical Hopf bifurcation. To validate the theory of the Hopf bifurcation, two reentry configurations are numerically studied. One is the Japanese capsule OREX, composed of a spherical cap facing forward and a reversed cone facing backward. With Mach number decreases in the reentry process for the capsule, the pitching motion would evolve from a point attractor to a periodic attractor, and the critical Mach number is about 2. 2 when the subcritical Hopf bifurcation occurs, the theory analysis and simulation result is in good agreement with the experiment and flight test results. The other configuration is a flat-nose winged double-cone body, with the decrease of Mach number, its pitching motion would evolve from a periodic attractor to a point a ttractor, and the critical Mach number at which the supercritical Hopf bifurcation occurs is about 6. 8. [ABSTRACT FROM AUTHOR]

Hypersonic boundary layer transitions caused by unsteady blowing and suction are investigated with linear stability analyses and direct numerical simulations (DNS). Three blowing–suction frequencies, i.e., 15, 30, and 45 kHz, are separately utilized to excite a pair of unsteady Görtler instability waves (the first two cases) or first-mode instability waves (the last case). These two primary instabilities, respectively, induce diamond-shaped and Λ-shaped structures through self-interactions. These structures are highly susceptible to high-frequency secondary instabilities, as is demonstrated by global Floquet analyses that take into account both temporal unsteadiness and spanwise spatial variations of the base flow. The secondary instability manifests as hairpin packets riding on the downstream end of the diamond-shaped structures or reside in the outward sides of the two legs of the Λ-shaped structures. The theoretical results quantitatively agree with the DNS results. Energy analyses further reveal that the wall-normal productions dominate the energy transfer for the secondary instability of the unsteady Görtler vortices, while the spanwise productions are crucial to the secondary instabilities in the first-mode oblique breakdown. Quasi-steady analyses based on the "frozen" base flow are also performed, whose results compare favorably with those from Floquet analyses in the lowest-frequency case. [ABSTRACT FROM AUTHOR]

Direct numerical simulation (DNS) is performed to study high-enthalpy effects on a turbulent boundary layer (TBL) over a curved compression corner. The post-shock flow state behind a wedge flying at Mach 20 and at an altitude of 30 km are chosen for the present simulation. The post-shock temperature is 3400 K, which is high enough to trigger chemical non-equilibrium of the air. A low-enthalpy case is used for comparison. The influences on the instantaneous structures of the streamwise velocity, temperature, and oxygen atoms are examined. The results show that the flow structures are similar on an upstream flat plate in both cases, while on a ramp, streaks of streamwise velocity fluctuations in the high-enthalpy case experience stronger shrink compared with that in the low-enthalpy case. Furthermore, streaks of temperature break into smaller ones when dissociation reactions are introduced. Qualitative and quantitative comparisons are made with the low-enthalpy case; performed using two-point streamwise wall-normal correlation, space–time correlation, and by comparing the propagation velocities of the fluctuations. The results of these analyses validate the observations about the instantaneous fluctuations and show that the differences in the propagation velocity are affected by convection effects and chemical reactions, and that the dissociation reactions accelerate the propagation of temperature fluctuations. [ABSTRACT FROM AUTHOR]

A systematic parametric study is presented on the modal global linear instability of Mach 6 boundary-layer flow over an inclined cone at a 6° angle of attack under typical wind tunnel conditions. The analysis is performed using the spatial BiGlobal theory. Results reveal two classes of global instabilities in the outboard region away from the leeward plane: high-frequency (hundreds of kHz) second mode instabilities and low-frequency (tens of kHz) crossflow instabilities. In the global eigenvalue spectra of the second mode instability, two distinct branches of significantly unstable modes are identified, namely, an approximately continuous spectrum (branch S) and a few discrete points (branch D). The branch D modes peak at the windward centerline, while branch S modes lie at a certain distance away from the windward meridian. The global stability characteristics of the crossflow instability over a conical configuration are uncovered for the first time. In the global eigenvalue spectra of the crossflow instability, many unstable modes emerge and form a complex pattern, with the most amplified frequency of around 30 kHz. The unstable crossflow modes are mainly distributed on the leeward side and wave angles obviously increase toward the leeward centerline. The peak growth rates are slightly smaller than those of second modes, and yet the most amplified frequency varies rather mildly along the streamwise direction so that they may achieve larger integrated growth rates than second modes do. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics predictions based on machine learning methods have become an important area of turbulence and transition research. However, the otherwise efficient and low-cost transition models based on Reynolds-averaged Navier–Stokes (RANS) methods have limited capability for dealing with hypersonic conditions, owing to the strong compressibility and multimodal features that are then present. This paper develops an augmented method for transition heat flux prediction. A deep neural network (DNN) is trained using flight test data from the China Aerodynamics Research and Development Center. The subject of the flight test is an inclined blunt cone on which temperature sensors are mounted. The training data consist of RANS solutions and flight test data, with the input being the mean strain/rotation rate tensor from RANS and the output the heat flux values from the flight test. The trained DNN model based on the RANS results can give heat flux values with similar accuracy to those from the flight test. For the blunt cone, the trained DNN model can accurately forecast the heat distribution caused by the Mack mode and the cross-flow transition under various inflow conditions, and the errors in the prediction results are all within 15%. Furthermore, the generalizability of the trained DNN model is also verified on an elliptic cone under different inflow conditions. This paper provides a new transition prediction approach with low computational cost and high accuracy. The proposed method solves the problem that the transition model fails in some working conditions and avoids re-modifying empirical criteria in the RANS model. It has both advantages of a transition model and flight tests and maintains the excellent potential for application. [ABSTRACT FROM AUTHOR]

Boundary layer transition (BLT) can cause a sharp rise in heat flux and skin friction, which can seriously affect the flight performance and safety of hypersonic flight vehicles. Therefore, the mechanism, prediction and control of transition have become important issues that must be dealt with for the development of advanced flight vehicles, and it is also a research hotspot of particular interest to major aerospace countries. Compared to other transition research approaches, model flight tests can better present the transition problems under real flight conditions, thus have been carried out extensively over the past 30 years. The United States, Germany, France, Australia, and other countries have carried out transition research based on flight tests, such as the Pegasus wing-glove crossflow transition and the Hypersonic Boundary Layer Transition (HyBOLT) transition control flight test of the United States, the joint research project of the Hypersonic International Flight Research and Experimentation-1 (HIFiRE-1) circular cone and the HIFiRE-5 elliptic cone transition flight tests between the United States and Australia, the flight test of compression surface transition of the scramjet forebody (LEA) in France and so on. Although these flight tests suffered various setbacks, they still obtained valuable transition data. Recently, the United States is carrying out the concave-surface transition flight tests of Hypersonic Boundary Layer Transition (BOLT) and BOLT-II. Since its first model flight test mission for verification purpose launched successfully in 2015, several hypersonic BLT flight tests have been conducted by China Aerodynamics Research and Development Center (CARDC). The flight tests have measured valid transition data under flight conditions, obtained the transition front and its dynamical variation on blunt cones at various angles of attack and a lifting body Hypersonic Transition Research Vehicle (HyTRV). The crossflow traveling waves in high-altitude flight were measured for the first time, and our understanding of hypersonic BLT has been greatly improved. [ABSTRACT FROM AUTHOR]

Understanding crossflow instabilities in three-dimensional boundary layers triggered by either traveling crossflow waves or stationary crossflow vortices is of great importance for modeling, predicting, and controlling hypersonic laminar-turbulent transition. However, due to very limited available flight experiment data, the crossflow instability under real flight conditions is still far from fully understood. To gain further insight, the raw data of a recent model flight experiment conducted by China Aerodynamics Research and Development Center have been thoroughly analyzed in the present study. The instrumented model is an inclined blunt cone mounted with several pressure sensors. Distinct low-frequency signals detected by these pressure sensors are peaked at about 10 kHz, which are in good agreement with the traveling-crossflow-wave frequencies with the largest N factors predicted by the eN method. Moreover, propagation velocities and wave angles of these signals obtained from correlation analysis also agree with the results from linear stability theory. The present study confirms that the detected low-frequency signals are traveling crossflow waves and provides the first evidence of traveling crossflow waves under real flight conditions. [ABSTRACT FROM AUTHOR]

Based on gas kinetic theory, a linear stability analysis method for low-speed rarefied flows was developed by Zou et al. ["A new linear stability analysis approach for microchannel flow based on the Boltzmann Bhatnagar–Gross–Krook equation," Phys. Fluids 34, 124114 (2022) and "A novel linear stability analysis method for plane Couette flow considering rarefaction effects," J. Fluid Mech. 963, A33 (2023)]. In the present study, we extended the method to high-speed rarefied flows using the Bhatnagar–Gross–Krook model. The Chebyshev spectral method is employed to discretize physical space, and the Gauss–Hermite and fourth-order Newton–Cotes quadrature methods are used to discretize velocity space. The fourth-order Newton–Cotes quadrature method was found to have sufficient accuracy for the stability analysis, laying the foundation for future research on hypersonic flows. The stability analysis of compressible rarefied Couette flow showed that acoustic modes are reflected between the wall and the relative sonic line, and the variation in their phase speed and growth rate with the wavenumber is not affected by the Mach number (Ma) and the Knudsen number (Kn). Increasing Kn has a stabilizing effect on both the acoustic and viscous modes, but as Ma increases, the attenuation rate of each mode's growth rate gradually decreases. In subsonic and sonic flows, the least stable viscous mode dominates in the case of small numbers. As Kn increases, the viscous mode gradually dominates over all wavenumber ranges considered in subsonic flow. In sonic flow, mode 1 is dominant in the region beyond the range of small wavenumbers. In supersonic flow, mode 2 is the least stable in the large wavenumber ranges, while mode 1 is the least stable in other wavenumber ranges. At a fixed wavenumber, as Kn increases, the decay rate of the growth rate of mode 2 is the highest. Additionally, under different Knudsen numbers, the growth rates of mode 1, mode 2, and the least stable viscous mode monotonically increase with an increase in Ma, with mode 2 showing the most significant increase. [ABSTRACT FROM AUTHOR]

In the present study, the influences of wall disturbances on coherent structures and the corresponding turbulent transport in supersonic turbulent boundary layers are investigated. The free-stream Mach number is set as 2.0. The database is scrutinized to present the instantaneous distributions and spectral properties of momentum and heat transfer related flow quantities. In their important roles in enhancing the momentum and heat transfer, the wall disturbances lead to the energetic turbulent fluctuations with the length scales of the wall disturbance wavelength and its harmonics in the near-wall region. The large-scale motions are also excited with the spanwise length scales of the turbulent boundary layer thicknesses, which, by reasoning, is caused by nonlinear interactions between wall disturbances and turbulent motions at some certain scales. They also produce intense density and pressure fluctuations that penetrate the boundary layer by deforming the sonic surfaces and radiate towards the free stream, where the fluctuations remain isentropic processes in nature. During this process, the steady wall disturbances are distorted by the turbulence, therefore endued with the features of multi-scale and multi-frequency instead of remaining energetic at a single wavelength or frequency. [ABSTRACT FROM AUTHOR]

In the present study, we investigate the evolution of turbulent statistics and coherent structures in hypersonic turbulent boundary layers at the Mach number of 5 impinged by oblique shock waves generated by the wedge with the angles of 14 ° , 10 ° , and 6 ° , inducing strong, mild, and incipient flow separation, by exploiting direct numerical simulation databases, for the purpose of revealing the underlying flow physics that are of significance to turbulent modeling. We found that the large-scale structures are amplified within the interaction zone, manifested in the form of large-scale low- and high-speed streaks with the spanwise length scale of boundary layer thickness, and gradually decay downstream, the process of which is extremely long. The abrupt variation in the characteristic length, time, and velocity scales as well as the incompatible viscous dissipation of the mean and turbulent kinetic energy results in the incorrect predictions by the Reynolds-Averaged Navier–Stokes (RANS) equation simulations, provided the models are established based on solving the transport equations of the turbulent kinetic equation and its viscous dissipation (k − ε or k − ω models, for instance). To amend this issue, we propose to refine the parameters in the model as the functions of wall pressure, the flow quantities related to multiple flow features. The RANS simulations with the k − ω SST model utilizing the proposed refinement improve greatly the accuracy of the skin friction, wall heat flux, and Reynolds shear stress downstream of the interaction zone, and the wall pressure distributions in hypersonic turbulence over compression ramp, suggesting its promising prospect in engineering applications. [ABSTRACT FROM AUTHOR]

This paper investigates the influences of the distribution of the grooves on the wall on the turbulent statistics, transport of turbulent kinetic energy, and flow structures in supersonic turbulent channel flows at the bulk Mach number of 3.0 by performing direct numerical simulations. It is found that the existence of the grooves leads to the enhancement of the turbulent kinetic energy close to the wall and the abatement thereof above the buffer layer. The density and temperature fluctuations are also enhanced, but only within the buffer layer, above which the influences of the grooves can be disregarded. The pressure fluctuations, however, are significantly increased, which is attributed to the radiated acoustic waves from the wall generated by the disturbances on the wall. Such inference is substantiated by the fact that the inclination angles of the phase averaged pressure are related to the Mach number. Nevertheless, the acoustic and dynamic processes seem to be decoupled, leading to insignificant pressure-dilatation terms in the transport of turbulent kinetic energy. [ABSTRACT FROM AUTHOR]

Görtler vortex-induced hypersonic boundary layer transition controlled by grooves is investigated using direct numerical simulations and spatial bi-global stability analysis. In the simulations, Görtler vortices are excited by wall steady blowing and suction with spanwise wavelengths of 3 mm. It is found that when the wall is covered with grooves, the Görtler streaks keep more regular even at the end of the model. In addition, the skin friction coefficient is reduced efficiently. Furthermore, the wall-normal and spanwise velocity shear are both reduced, suppressing growths of secondary instabilities. In conclusion, grooves can delay Görtler vortex-induced transition by modifying the Görtler streaks structure and instability, which would shed light on hypersonic boundary layer transition control. [ABSTRACT FROM AUTHOR]

The traditional method for obtaining aerodynamic parameters of airfoils by solving Navier–Stokes equations is a time-consuming computing task. In this article, a novel data-driven deep attention network (DAN) is proposed for reconstruction of incompressible steady flow fields around airfoils. To extract the geometric representation of the input airfoils, the grayscale image of the airfoil is divided into a set of patches, and these are input into the transformer encoder by embedding. The geometric parameters extracted from the transformer encoder, together with the Reynolds number, angle of attack, flow field coordinates, and distance field, are input into a multilayer perceptron to predict the flow field of the airfoil. Through analysis of a large number of qualitative and quantitative experimental results, it is concluded that the proposed DAN can improve the interpretability of the model while obtaining good prediction accuracy and generalization capability for different airfoils and flow-field states. [ABSTRACT FROM AUTHOR]

In the present study, we perform direct numerical simulations to investigate the spatial development and basic flow statistics in the supersonic turbulent boundary layers at the free-stream Mach number of 2.0 over smooth and disturbed walls, the latter of which enforces extra Reynolds shear stress in the streamwise direction to emulate the drag increment and mean streamline curvature effects of rough walls. Such disturbances escalate the growth rate of turbulent boundary layer thickness and the shape factor. It is found that under the rescaled global coordinate, the mean velocity, Reynolds stress, and pressure fluctuation variance manifest outer-layer similarity, whereas the average and fluctuation variances of temperature and density do not share such a property. Compressibility effects are enhanced by the wall disturbances, yet not sufficiently strong to directly impact the turbulent kinetic energy transport under the presently considered flow parameters. The generalized Reynolds analogy that relates the mean velocity and temperature can be satisfied by incorporating the refinement in modifying the generalized recovery coefficient, and that associates the fluctuating velocity and temperature work reasonably well, indicating the passive transport of temperature fluctuations. The dispersive motions are dominant and decay exponentially below the equivalent sand grain roughness height ks, above which the wall disturbances are distorted to form unsteady motions responsible for the intensified density and pressure fluctuations in the free-stream traveling isentropically as the acoustic radiations. [ABSTRACT FROM AUTHOR]

Wall temperature is a crucial factor for the transition of hypersonic boundary layers. This paper investigates the wall temperature effects on the hypersonic boundary-layer transition over an inclined blunt cone with two wall temperatures by direct numerical simulations and instability analysis. The breakdown processes of leeward streamwise vortices and crossflow vortices are both studied. Inner modes with lower phase velocities and outer modes with higher phase velocities are responsible for the breakdown of leeward streamwise vortices, respectively, in cooled- and heated-wall cases. A higher wall temperature will promote the boundary layer transition in the vicinity of the leeward centerline due to the collision of nearby crossflow vortices with the leeward mushroom structure, instead of by destabilizing inner and outer modes. In the crossflow-dominated region, the transition is triggered by the interaction between second modes and crossflow vortices for the cooled-wall case. Increasing the wall temperature will promote the transition in this region even though second modes are suppressed. [ABSTRACT FROM AUTHOR]

In this work, we carried out roughness-resolved direct numerical simulations of cube-roughened turbulent channel flows to investigate the effects of aligned and staggered arrangements, element spacings, and element orientations on the statistics of rough-wall turbulence. The results show that the equivalent sandgrain roughness, Reynolds stresses and dispersive stresses are affected by element spacings and arrangements in different ways depending on the cube orientations. Placing the roughness elements in a staggered way in general increases the equivalent sandgrain roughness, unless when the element–element interaction is insignificant for the cube orientation with wakes of short length. As for the Reynolds normal stresses and the streamwise component of the dispersive stresses (both are normalized by the total friction velocity), placing the cube elements in a staggered way decreases their maximal values when compared with the aligned arrangements. As for the effects of element spacing on the equivalent sandgrain roughness and the maximums of the Reynolds normal stresses, similar trends are observed for different element orientations and arrangements when increasing the element spacing l/r (where r is the cube height) from 2.0 to 2.8. When further increasing the element spacing l/r from 2.8 to 3.5, however, different trends are observed for different element orientations. As for the dispersive stresses, greater maximal values of their streamwise components are observed for larger element spacing for all the considered cube-roughened surfaces. For the turbulence statistics in the wake of the cube element, certain similarities are observed for different element spacings. [ABSTRACT FROM AUTHOR]

• An enhanced strategy for adaptive Cartesian grid generation is proposed. • A rapid Cartesian-triangle intersection determination method is developed. • The efficiency of Cartesian grid generation for complex 3D geometry is assessed. • An improved backtracking algorithm for minimum distance query is described. This article presents an enhanced strategy for generating Cartesian grids for arbitrary complex three-dimensional (3D) geometry. It addresses the major challenges, including data structures managing surface triangles and Cartesian cells, background Cartesian generation, intersection cell determination, and adaptive mesh refinement. To overcome the problem of inefficiency, we developed a robust method for determining intersecting cells based on the k-dimensional tree data structure combined with the fast 3D-Cartesian box-triangle overlap testing algorithm. Furthermore, the minimum distance query algorithm based on the k-dimensional tree was enhanced to improve the query efficiency by reducing the number of backtrackings. The correctness and efficiency of the proposed strategy were evaluated and verified by 3D tests on different configurations. The results show that in terms of mesh generation, the CPU time ∕ cell was nearly 5.33–5.54×10−6 s; in terms of the minimum distance query, the query efficiency of the improved backtracking method improved by up to 870.9 times compared with the traversal method. Meshing experiments of several complicated configurations demonstrated that the proposed algorithms were accurate, robust, and efficient. At last, an example was examined, and the result demonstrates that the mesh generation strategy developed in this study meets the actual flow field calculation requirements. [ABSTRACT FROM AUTHOR]

The effects of nose bluntness on the entropy-layer stabilities in hypersonic flows over blunt cones and wedges are investigated by using linear stability theory and numerical simulation. The entropy-layer instabilities of blunt wedges are stronger than those of blunt cones. The unstable mode frequency of the entropy layer decreases with increasing bluntness due to a thicker entropy layer. Larger bluntness is effective at widening the region of the unstable mode downstream, creating more opportunities for entropy-layer disturbances to force the triggering of boundary layer transition. Numerical simulations show that the entropy-layer mode can excite the first mode of the boundary layer. [ABSTRACT FROM AUTHOR]

In the present study, we investigate influences of shock intensity on wall pressure fluctuations by performing direct numerical simulations of supersonic turbulence boundary layers over compression ramps with different turning angles. We found that as the turning angle increases, low-frequency motions of the separation shock are enhanced, accompanied by enlarged energetic pressure structures with lower convection velocities. By inspecting wavenumber-frequency spectra under the assumption of streamwise homogeneity, we further identified two energetic modes convected at different velocities. The one with the lower convection velocity, namely, the "slow mode," inherited from the upstream pressure fluctuations of the turbulent boundary layer, is decelerated when passing through the oblique shock, during which the "rapid mode" with pressure fluctuations convected at higher speeds are generated. The increasing turning angle decelerates the slow mode and intensifies the fast mode. The reconstruction of the flow field suggests that the rapid mode is associated with the shear layer generated adjacent to the interaction zone, while the slow mode is associated with the Görtler vortices on the ramp. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of a supersonic turbulent boundary layer on a flat plate interacting with an impinging shock wave are carried out with two different incident shock angles at Mach 2.25. The effect of the interaction strength on the recovery process in the downstream region is systematically studied, including the turbulence evolution, the statistical and structural properties of wall pressure fluctuations, and the generation of mean skin friction and wall heat flux. The variations of the Reynolds stress components, the anisotropy tensor, and the turbulent kinetic energy budget in the two flow cases highlight a slow reversal tendency and an increasingly pronounced importance of the outer-layer large-scale structures in the relaxation region of the strong interaction. We find that the effect of increasing the interaction strength on the fluctuating wall pressure is reflected by a decrease in the characteristic frequencies, an increase in the spatial extent, and a decrease in the convection velocity. We decompose the mean skin friction and wall heat flux into different physically informed contributions and reveal that the mean wall heat flux generation is the same regardless of the interaction strength; in contrast, the generation mechanism of mean skin friction is found to be fundamentally changed. A novel scale-decomposition method is used to quantify the effect of the increased interaction strength on the leading components, and it is demonstrated that the energetic outer-layer large-scale structures are the dominant contributor in the recovery process as the interaction strength is increased. [ABSTRACT FROM AUTHOR]

Microchannels are important components of microelectromechanical systems (MEMSs) that encounter rarefaction effects due to their small-scale characteristics. The influence of rarefaction effects on the flow stability of microchannels should be investigated to improve MEMS performance. Based on kinetic theory, a linear stability analysis approach for low-speed rarefied flows was developed by using the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation with an external force term. This approach was applied to study the linear temporal stability of microchannel flows. A slip flow model was introduced for comparison. The corresponding eigenvalue problem was solved with a Chebyshev collocation method. This novel approach yielded a critical Reynolds number of 5778. Analysis of the validity and accuracy of the slip flow model shows that although this model cannot capture the Knudsen layer structure, this approach effectively improves the prediction accuracy of the growth rate of the least stable mode. However, the prediction accuracy gradually decreases with increasing Knudsen number. Compared with the stability results obtained from the BGK equation, the Navier–Stokes equations-based stability analysis method always underestimates the disturbance growth rate, regardless of whether a slip flow model is used. The stability analysis results show that rarefaction effects stabilize the flow. The degree of rarefaction does not affect the trends of growth rate and phase velocity with wavenumber, nor does it affect the shape of the velocity eigenfunctions. For a rarefied case, increasing the Mach number has a destabilizing effect on low-speed microchannel flows. [ABSTRACT FROM AUTHOR]

The wind tunnel experiment is an important approach to studying boundary layer transition. In this study, the effects of bluntness, unit Reynolds number, and wall temperature ratio on hypersonic conical boundary layer transition were studied using numerical simulations and linear stability analyses based on the wind tunnel experimental data. Through the flow similarity principle, the treatment of the bluntness-varying problem was determined. Combining the experimental transition data and theoretical analysis results of sharp and blunt cones at home and abroad, the relation between the transition factor N t r and the unit Reynolds number before ' N factor reversal', as well as the relation between the transition value R t r and the unit Reynolds number from ' N factor reversal' to 'transition reversal' were determined too. Finally, according to the wind tunnel test data of China Aerodynamics Research and Development Center, the effect of wall temperature ratio on the receptivity of blunt-cone boundary layer was stated out, and the correlation of transition Reynolds number under different wall temperature ratios was determined. The influence law of parameters in this correlation was also determined. • A correlation method of wind-tunnel experimental transition is developed to quantify the effects of flow parameters. • The correlation of the receptivity including wall temperature ratio and nosetip Reynolds number is developed. • The correlation formula between transition factor N t r and unit Reynolds number is given. [ABSTRACT FROM AUTHOR]

Direct numerical simulations are carried out to identify the effects of shock impingement on the behavior of bump flow at freestream Mach number of 2.25. Two cosine-shaped bump cases, with and without an impinging oblique shock at an angle of 33.2°, are compared. The shock impingement exhibits a remarkable influence on the pattern of the shock system and on the size of the separation region. A spectral analysis finds that low-frequency unsteadiness is significantly enhanced by the impingement interaction, and the proper orthogonal decomposition highlights the low-frequency breathing motion of the separation bubble, which is accurately reconstructed using only the first ten low-order modes. Downstream of the bump, both the Reynolds stress components and the turbulence kinetic energy exhibit a general amplification, with the peaks reoccurring at outer wall-normal locations. A turbulent kinetic energy budget analysis shows the greatly increased production in the outer layer which is balanced by turbulent transport and dissipation. An anisotropy-invariant map analysis identifies enhanced isotropic turbulence in the vicinity of the bump, which is qualitatively modified into a two-component axisymmetric state around the reattachment point. In addition, the mean skin friction decomposition suggests that the shock impingement has little influence on the predominant contribution of turbulence kinetic energy production, apart from the spatial growth dominance at the bump summit in the absence of the impinging shock. Interestingly, a scale-decomposed analysis quantitatively demonstrates that the contributions of small-scale structures are attenuated, but those of large-scale ones are relatively increased, with a contribution of more than 80% with shock impingement. [ABSTRACT FROM AUTHOR]

Direct numerical simulation of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.25 and a friction Reynolds number of Reτ = 769 subjected to an expansion corner with a deflection angle of 12° is performed to investigate the effect of expansion on the characteristics of the wall heat flux (WHF). The effect of expansion on the statistical and structural properties of the fluctuating WHF is analyzed systematically in terms of probability density function, frequency spectra, and space-time correlations. Normalization using the local root mean square value yields good collapse of the probability density function curves. Unlike with wall pressure frequency spectra, it is found that expansion has little influence on the low-frequency components of the WHF spectrum. The correlation results show that the main effect of expansion is to increase the characteristic length scales and convection velocity of the WHF fluctuation in the post-expansion region. Furthermore, a direct comparison between the conditionally averaged flow fields and those presented in the authors' previous work [Tong et al., Phys. Fluids 34, 015127 (2022)] is performed to uncover the effect of expansion on the flow structures associated with extreme positive and negative WHF fluctuation events. We highlight that the extreme positive event emerges below a small hot spot under the action of a strong Q4 event, whereas the extreme negative event is relatively insensitive to expansion and still occurs between a pair of strong oblique vortices. In addition, we decompose the mean WHF into seven physics-informed contributions and quantify the effect of expansion on the dominating components with the aid of the bidimensional empirical mode decomposition method. The scale-decomposed results demonstrate quantitatively that expansion decreases the contribution of the large-scale structures in the outer region but the small-scale structures in the near-wall region contribute heavily to the mean WHF generation in the downstream region. [ABSTRACT FROM AUTHOR]

In the present study, we propose a hybrid numerical method for wall-resolved large-eddy simulation of compressible wall-bounded turbulence. Based on the hierarchical feature of energetic structures in wall-bounded turbulence, we propose to solve the convective term in the near-wall region with the low-dissipative kinetic energy preserving scheme to resolve the small-scale structures and the upwind scheme away from the wall to avoid strong numerical oscillations generated by the spurious errors. Two parameters are introduced in this method, one related to the transition point yp+ and the other the transition range α. By a series of well-designed test cases, we identify that setting yp+ as the streamwise grid interval Δx+ gives the best results, whereas the effects of the variation of α are marginal. By further performing simulations at higher Reynolds numbers and Mach numbers, we prove that the presently proposed method is capable of accurately predicting the skin friction, mean velocity and temperature and velocity fluctuation intensities and, in the meantime, retaining numerical stability. [ABSTRACT FROM AUTHOR]

The purpose of this work is to improve the efficiency of sample selection with the recursive method for wall-bounded turbulent flows. In the proposed physics-assisted recursive method, the flow field is divided into several sub-regions along the wall distance. Since the distributions of the flow variables have certain similarity along the wall normal direction, fast clustering of similar data can be achieved, which paves the way for the rapid elimination of redundant data. Then, the recursive method is used for sample selection in each sub-region. The effectiveness of the proposed method is investigated through several cases. The results show that the proposed method has good convergence and grid independence and improves the computational efficiency of the recursive method for sample selection. Since the amount of training data is reduced, the time consumption of model training is decreased. In addition, it is demonstrated that sample selection can also be helpful to achieve more balanced model performance by changing the distribution of training data. [ABSTRACT FROM AUTHOR]

The negative and positive fluctuations of wall shear stress τ ′ x and wall heat flux q ′ w can be related to the wall-attached paired up large-scale velocity and temperature streaks. It is justifiable to infer the spatially paired-up coexistence of those wall flow quantities. The present study aims at testifying this hypothesis. We establish such relations between the negative and positive wall shear stress by exploiting a direct numerical simulation database over heated and cooled walls at the friction Reynolds number of 800 and the Mach number of 2.25. The clustering method is adopted for the search of the in-pair structures. It is found that the τx- and qw-structures are less self-similar for flows over cold walls. As they become wider, the τx-structures are increasingly more streamwise stretched, while the trend is reversed for qw-structures. τx-structures of opposite signs are paired up and aligned in the spanwise directions as the wall-attached streamwise velocity, and are left behind by streamwise rollers. The relative position between qw-structures of opposite signs, on the other hand, is sensitive to the wall temperature. Scrutinizing the statistical structures, we elucidate that such spatial coherence is determined by the meandering of velocity streaks that yields strong streamwise gradients of the streamwise velocity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the differences in wall heat transfer between the low- and high-enthalpy turbulent boundary layers by exploiting direct numerical simulation databases of hypersonic turbulent boundary layers at the free-stream Mach number of 4.5 and the friction Reynolds number of 800. For that purpose, we refine the integral formula of decomposing the wall heat flux proposed by Sun et al. ["A decomposition formula for the wall heat flux of a compressible boundary layer," Adv. Aerodyn. 4, 1–13 (2022)], enabling us to scrutinize the contribution of different physical processes. Statistical results show that the mean wall heat transfer is primarily contributed by the heat conduction, the turbulent heat transfer, viscous dissipation of mean kinetic energy, and turbulent kinetic energy production. Among these processes, the contribution of the turbulent heat flux in the high-enthalpy case is 10% higher than that in the low-enthalpy case. Such discrepancy is caused by the turbulent–chemistry interaction consisting of velocity and species mass fraction fluctuations. Coherent structures in the conditionally averaged fields related to this process reveal that the sweep in the viscous sublayer and ejection in the logarithmic layer bringing the hot fluid downward and upward, respectively, significantly alter the distribution of the species mass fraction. The wall heat flux fluctuations are slightly enhanced in the high-enthalpy flows, which is ascribed to be the intensification of traveling wave packets. [ABSTRACT FROM AUTHOR]

Computational Fluid Dynamics (CFD) has become an indispensable tool in the optimization design, and evaluation of aircraft aerodynamics. However, solving the Navier-Stokes (NS) equations is a time-consuming, memory demanding and computationally expensive task. Artificial intelligence offers a promising avenue for flow field solving. In this work, we propose a novel deep learning framework for rapidly reconstructing airfoil flow fields. Channel attention and spatial attention modules are utilized in the downsampling stage of the UNet to enhance the feature learning capabilities of the deep learning model. Additionally, Embedding the predicted values of the deep learning model as initial values into the CFD solver to accelerate its iterative convergence. The NACA series airfoils were used to validate the prediction accuracy and generalization of the deep learning model. The experimental results represent the deep learning model achieving flow field prediction speed three orders of magnitude faster than CFD solver. Furthermore, the CFD solver integrated with deep learning model demonstrates a threefold acceleration compared to CFD solver. By extensively mining historical flow field data, an efficient solution is derived for the rapid simulation of aircraft flow fields. [ABSTRACT FROM AUTHOR]

We studied the stability of leeward streamwise vortices over a hypersonic inclined blunt cone under a flight condition by solving the two-dimensional spatial eigenvalue problem (BiGlobal) and plane-marching parabolized stability equations (PSE3D). The stability analyses were performed based on the laminar flow obtained by direct numerical simulation. Due to the azimuthal pressure gradient and large bluntness, a pair of large-scale inward vortices dominate in the vicinity of the leeward ray. Such vortical structures are different from previous studies, where outward vortices are most prominent. Two types of unstable modes are identified, namely, "inner mode" with low phase velocities and "outer mode" with high phase velocities. The inner modes are unstable in a wide frequency range compared to the outer modes, differing from previous studies where inner modes are deemed to lie in a much lower frequency range compared to the outer modes. Moreover, the inner modes, with supersonic phase velocities, are found to be able to radiate weak acoustics outside the vortices. Mack mode, belonging to the outer-mode instability, is most amplified that it is likely responsible for the breakdown of the vortices. BiGlobal and PSE3D results show good agreement regarding the downstream developments of the Mack mode and inner modes and yet exhibit remarkable discrepancies in tracing the evolution of the outer modes, highlighting the necessity of considering the non-parallel effects when studying the stability of streamwise vortices. [ABSTRACT FROM AUTHOR]

This two-part study investigates the effects of Mach number and wall temperature on the statistics of wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence. In the first part, we focus on their one-point statistics, including the root mean square (r.m.s.), skewness factor (third-order moment), flatness factor (fourth-order moment), and their correlations. By exploiting the direct numerical simulation databases, we found that the r.m.s. of the streamwise wall shear stress and pressure, the skewness factor of all the flow quantities considered, and the flatness factor of streamwise wall shear stress monotonically vary with the friction Mach number ( M τ ), while for the rest, the wall heat flux and global temperature parameters should be taken into account as well for a monotonic trend of variation. The correlation coefficients between wall shear stress, pressure, and heat flux fluctuations increase with the Mach number M τ , suggesting the underlying interactions between dynamic and thermodynamic processes. The distributions of spectra and probability density functions indicate that the increased correlation is induced by the highly intermittent traveling wave packets among the streaky structures, as reflected by the "double-peak" feature of the spectra that gradually emerges with the increasing compressibility effects. The probability density distribution also manifests the alteration of the occurrence of extreme events caused by these structures. By accordingly decomposing the fluctuations with cutoff filtering, it is found that the root mean squares of streamwise wall shear stress and heat flux fluctuations related to the streaky structures are Mach number-independent, while those related to the traveling wave packets monotonically increase with the friction Mach number. [ABSTRACT FROM AUTHOR]

In the present study, we investigate two-point statistics of fluctuating streamwise wall shear stress τ ′ x and wall heat flux q ′ w by exploiting a direct numerical simulation database of supersonic turbulent boundary layers over a heated wall and a cooled wall at the friction Reynolds number around 800. By separately investigating positive and negative families of τ x ′ and q w ′ with the aid of the conditional correlation analysis, we identify the asymmetrical deformation of τ ′ x and q ′ w , reminiscent of and ascribed to the asymmetrical deformations of sweeps and ejections events. The degree of such asymmetry is alleviated by the lower wall temperature. The spatial orientation of τ x ′ is insensitive to the wall temperature, whereas the spanwise elongated q ′ w that is closely related to the wall pressure is manifested merely in the cooled-wall case. The cross correlation between τ x ′ and the fluctuating streamwise velocity u′ reveals that low-speed streaks related to negative τ x ′ are more inclined to the wall than high-speed ones related to positive τ x ′ by 4 ° – 5 ° , and that the phase lag between negative τ x ′ and u′ is larger than that between positive τ x ′ and u′ except in the near-wall region. Such a difference is proportional to the wall distance and should be considered for models predicting near-wall and wall quantities using signals in the logarithmic layer. [ABSTRACT FROM AUTHOR]

Wall disturbances in high-speed turbulent boundary layers induce large-scale motions in the outer region even when the Reynolds number is not sufficiently high for their existence in the case of smooth wall flows. In the present study, we investigate the dynamics of these outer region large-scale motions by exploiting the scale-by-scale energy transport in the spectral space. By scrutinizing the disparity in the budget terms of the turbulent kinetic energy spectra between turbulence over smooth and disturbed walls, we found that the intensification of the large-scale motions in the outer region is statistically correlated with the stronger interaction between the Reynolds stress and the mean shear, i.e. the production term of the turbulent kinetic energy. The corresponding turbulent kinetic energy is then transferred to smaller-scale motions and dissipated by viscosity, whereas the effects of spatial diffusion and mean convection are insignificant and are dimly affected by the wall disturbances. These dynamic processes are roughly irrelevant to the Mach numbers, and processes related directly to the genuine compressibility effects, namely the dilatational motions and mass flux, are trivial. The outer large-scale motions contribute to the skin friction by approximately 19% ∼ 45% compared with 4% in smooth wall cases in terms of the mean kinetic energy transport, suggesting that the drag increment in turbulent boundary layers in the presence of wall disturbances should be partly attributed to their intensification. • Large-scale motions are stronger in supersonic turbulence with wall disturbances. • Turbulent kinetic energy transport in the spectral space is analysed. • The large-scale intensification is related to the turbulent production. • Large-scale motions contribute highly to skin friction disturbed wall cases. [ABSTRACT FROM AUTHOR]

Studies on the stability of Rayleigh-Bénard convection in rarefied gases mainly focus on monatomic gases, whereas diatomic gases are the prevailing medium in actual flows. This paper conducts a study on the Rayleigh-Bénard convection stability of diatomic rarefied gases based on the Navier-Stokes (NS) equations modified with slip boundary conditions. We aim to elaborate the effects of different molecular interaction models and flow parameters (Knudsen number Kn , Froude number Fr , Prandtl number Pr , etc.). And several interesting phenomena have been discovered: (1) Compared with monatomic gases, the instability region of diatomic gases expands towards higher Knudsen numbers and smaller Froude numbers; (2) It is generally believed that increasing rarefaction leads to flow stabilization. However, we have found that in the case of small wave numbers within the scope of our research, the rarer the gas, the higher the growth rate, which contradicts traditional cognition; (3) Competition mechanism between buoyancy and gravity in the stability of Rayleigh-Bénard convection exists; (4) When considering the variations of Prandtl number and specific heat ratio with temperature, the relative deviation of the growth rate of the most unstable mode is significant. • This study explores the instability of Rayleigh-Bénard convection in rarefied gases, with a focus on diatomic gases. • Contrary to conventional beliefs, increased rarefaction results in higher growth rates for small wave numbers as Knudsen number increases. • Competition mechanism between buoyancy and gravity: when buoyancy and gravity are equivalent, the flow is more prone to instability due to non-monotonic changes in density distribution. • Diatomic gases show an extended instability region compared to monatomic gases, reaching larger Knudsen numbers and smaller Froude numbers. [ABSTRACT FROM AUTHOR]

Hypersonic turbulence over disturbed walls can be encountered when the fuselage of the vehicles is ablated or installed with transpiration-cooling porous media, resulting in the variation of the wall heat transfer that complicates its accurate predictions. In this paper, we study the turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers at the free-stream Mach number of 6.0 subject to wall disturbances with different wall temperatures, with our focus on the compressibility effects. We found that the temperature fluctuation intensity and the turbulent heat flux are enhanced in the outer region, which is attributed to the higher mean temperature gradient induced by the wall disturbances. The solenoidal and dilatational components of the turbulent heat flux, obtained by the Helmholtz decomposition that splits the velocity fluctuations into the solenoidal and dilatational components, are of opposite signs, with the latter smaller in magnitude but showing the tendency of mitigating the former. The integration formula that decomposes the wall heat transfer into various physical processes reveals that the viscous dissipation generates the wall heat transfer, while the turbulent heat flux, work of pressure on dilatation and the mean flow convection transport it towards the free stream. The contribution of the dilatational motions to the viscous dissipation and turbulent heat flux is negligible compared with that of the solenoidal components. [ABSTRACT FROM AUTHOR]

We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M∞ = 2.25 and a Reynolds number Reτ = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature Tw/Tr = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space–time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Reτ similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon ["Extremely high wall-shear stress events in a turbulent boundary layer," J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. ["Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions," J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions. [ABSTRACT FROM AUTHOR]

The receptivity of the second mode for Mach 6 flow over a blunt wedge with a nose radius of 0.258 mm is investigated numerically. When a plane slow acoustic wave is imposed on the freestream, the receptivity process of the boundary layer goes through three stages, with the development of an entropy-layer mode, a fast mode, and nonmodal external disturbances, before exciting the second mode. The first two dominant modes can be obtained by linear stability theory in the entropy layer and the boundary layer, respectively, whereas the third is a complicated type of disturbance whose shape function peaks in the entropy layer. The results show that the nonmodal disturbances in the entropy layer play a leading role in the excitation of the second mode, which suggests that the growth of nonmodal disturbances could dominate nonmodal amplification, eventually leading to boundary-layer transition. [ABSTRACT FROM AUTHOR]

A new type-II secondary instability mode was recently identified in high-speed cross-flows using stability analysis, but its role in the transition process is not yet clear. Here, the breakdown of stationary cross-flow vortices at high speeds is examined using direct numerical simulation to determine differences from the low-speed case. The transition is achieved by disturbing stationary cross-flow vortices with unsteady blowing/suction in a swept-wing boundary layer with swept angle 45°, free-stream Mach number 6, and unit Reynolds number 8 × 10 6 . The results reveal that, as in low-speed cases, the type-I secondary instability mode (with frequency ≈ 190 kHz) is crucial to the breakdown, but neither the traditional nor the new type-II secondary instability play a role. The vortical structure induced by the type-I secondary instability mode has two counter-rotating tubes stretched along the spanwise direction and a footprint aligned normal to the mean flow direction. The composite vortex structures are similar to rolls/braids in plane free-shear layers arising from Kelvin–Helmholtz instability and they evolve into hairpins in the late stage of the transition. Some preliminary statistics from a three-dimensional turbulent boundary layer are provided as a comparison to the two-dimensional ones. The fluctuating cross-flow velocity does not contribute to the momentum and heat transfer on average, probably due to the very weak mean cross-flow profile. Thus, the obtained three-dimensional turbulent boundary layer is the same as the two-dimensional one but inclined by a swept angle. To the authors' knowledge, this is the first in-depth analysis of the high-speed cross-flow transition to full turbulence. [ABSTRACT FROM AUTHOR]

Cartesian meshes based on the immersed boundary method are widely adopted for their convenience in implementing automated mesh generation. The performance of Cartesian mesh generation, particularly for complex geometries, is a crucial factor that directly impacts the efficiency of computational fluid dynamics solutions. In this study, we present an innovative strategy for efficient Cartesian mesh generation. Our methodology centers around the inner product test (IPT), enabling precise and efficient interior/exterior determination for intersected Cartesian cells. For this purpose, we enhance the k-d tree based intersection determination process to provide essential information of surface mesh for IPT, while concurrently improving the efficiency of the determination process. Our new methods offer automatic generation capabilities for arbitrary complex geometries. Through a series of tests, the new methods illustrate the notable performance improvements with the generation time of less than 4 min for the Cartesian mesh with 108 cells. Overall, our work optimizes Cartesian mesh generation for complex geometries, presenting significant potential for addressing the challenges of moving boundary problems. [ABSTRACT FROM AUTHOR]

In this paper, a direct numerical simulation is performed to study the wake structures of a micro-ramp vortex generator in the hypersonic flow. The whole evolution process of vortical structures of the wake flow has been carefully analyzed. First, the scaling laws for the profiles of mean velocities and fluctuations have been explored. The results show that the scaling laws based on the supersonic experiments can be directly applied in the hypersonic wake flow with a few discrepancies near the wall. Then, the detailed structures of arc-like vortices are examined, and the legs of vortices are found not being connected with each other. No full vortex ring is detected in the present simulation. At the downstream of the wake flow, the intensity of arc-like vortices has been augmented when passing the separation shock. The results reveal that a vortex train composed of arc-like vortices and shear layer is formed. With the help of the proper orthogonal decomposition, the impact of arc-like vortices on the heat flux has been revealed. The alternative positive and negative strips in the streamwise direction suggest the impinging process of arc-like vortices. The frequencies of the corresponding modes further prove that the strips are the footprint of arc-like vortices. [ABSTRACT FROM AUTHOR]

The wall temperature significantly varies the turbulent statistics and coherent structures in high-speed wall-bounded turbulence under the low-enthalpy condition. The present study set out to investigate whether this is also the case for high-enthalpy turbulent boundary layers that incorporate the chemical reactions of multi-species gas mixture. For that purpose, we perform direct numerical simulations for high-enthalpy turbulent boundary layers at the Mach number of 4.5 and the momentum Reynolds number of 2400 with three groups of wall temperature. Statistical results show that the effects of wall temperature on the mean flow properties are similar to those of low-enthalpy flows, and the chemical reactions only affect the mean temperature without leaving strong impacts on the statistics of velocity. The wall heat flux and the physical processes thereof are further analyzed. The mass diffusion effects are increased by the rising wall temperature due to the more sufficient dissociation of the molecules. The wall heat flux fluctuations are also slightly enhanced, with the lower skewness and the higher kurtosis, and show more prominent structures of traveling wave packets and weaker streaks, as well as the less coherent vortices in the vicinity of the extreme positive wall heat flux events. The organizations of the mass species are also altered substantially by the rising wall temperature due to the stronger impacts of chemical reactions on the flow dynamics. [ABSTRACT FROM AUTHOR]

In order to obtain the information about flow field, traditional computational fluid dynamics methods need to solve the Navier-Stokes equations on the mesh with boundary conditions, which is a time-consuming task. In this work, a data-driven method based on convolutional neural network and multi-head perceptron is used to predict the incompressible laminar steady sparse flow field around the airfoils. Firstly, we use convolutional neural network to extract the geometry parameters of the airfoil from the input gray scale image. Secondly, the extracted geometric parameters together with Reynolds number, angle of attack and flow field coordinates are used as the input of the multi-layer perceptron and the multi-head perceptron. The proposed multi-head neural network architecture can predict the aerodynamic coefficients of the airfoil in seconds. Furthermore, the experimental results show that for sparse flow field, multi-head perceptron can achieve better prediction results than multi-layer perceptron. [ABSTRACT FROM AUTHOR]