Conical gas flows with shock waves and turbulent boundary layer separation

The results of a theoretical and experimental investigation of nonsymmetric flow around a V-wing with supersonic leading edges are presented. The range of the angles of attack and yaw, on which additional singular lines are formed on the windward cantilever of the wing, are experimentally determined using different techniques of flow diagnostics. These are one convergence line and two divergence lines in the transverse flow which were not previously observable in the calculations of ideal-gas flow around wings. It is established that the appearance of the three new alternating singular lines located between the central chord of the wing and a convergence line, exterior to them and occurring within the framework of the ideal gas model, is associated with the relation between the intensities of two contact discontinuities. One of these proceeds from the branching point of the bow shock above the leeward cantilever, while the second issues out of the triple point of a λ-shaped shock configuration accompanying developed turbulent-boundary-layer separation generated by an internal shock incident on the leeward cantilever surface. If the intensity of the contact discontinuity proceeding from the branching point of the bow shock is large as compared with that of the contact discontinuity of the λ-configuration, then the flow pattern realized on the windward cantilever is analogous to that obtained within the framework of the ideal gas model, that is, it includes one convergence line on the wing surface. Under these conditions, the results of the calculations within the framework of the ideal gas model are applicable for understanding the phenomena occurring in the wing shock layer in a considerable part of the control parameter range, including the regimes with intense internal shocks generating turbulent boundary layer separation from the leeward cantilever. Corrections should be made only for a carachteristic pressure distribution in the separation zone and, as a consequence of separation, for an elevated pressure level in the vicinity of the central chord which is the stagnation line of the transverse flow that has passed across the oblique and terminating shocks of the λ-configuration and possesses a higher stagnation pressure than the flow that has passed in an ideal gas across the internal shock incident normally on the leeward cantilever. This is possible only when the divergence line, at which the stream surface enclosing the turbulent boundary layer separation zone enters, does not go over from the leeward onto the windward cantilever.     

Structure of supersonic inviscid nonsymmetric conical flow around a V-wing

The shock wave structure of flow around a V-wing and its properties determining the conical flow topology are numerically investigated within the framework of the inviscid gas model on a wide range of the angles of attack and yaw when in the disturbed supersonic flow either nonsymmetric Mach interaction between the shocks attached to the leading edges of the wing or a shockless flow in the compressed layer on the windward cantilever is realized. The subranges of the angles of attack and yaw with the disturbed flow properties characteristic of the wing of the given geometry are determined. It is found that at high angles of attack, when the branching point of the bow shock beneath the leeward cantilever generates an intense contact discontinuity, the structure of the conical flow in the shock layer on the windward cantilever involves a singularity of a new type which can be characterized as a “vortical” Ferri singularity. It is located above the point of convergence of the streamlines proceeding from the leading edges of the wing, at the vertex of the corresponding contact discontinuity. Flow patterns with the point of convergence of the streamlines proceeding from the leading edges located in the elliptical flow region, which is placed at a local maximum of the pressure distribution over the surface are also found. The range of the angles of attack and yaw on which this new property of supersonic conical flows is realized in the presence of a branched shock system is determined.     

Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

The results of an experimental and numerical investigation of flow and heat transfer in the region of the interaction between an incident oblique shock and turbulent boundary layers on sharp and blunt plates are presented for the Mach numbers M_∞ = 5 and 6 and the Reynolds numbers Re_∞L = 27×10⁶ and 14×10⁶. The plate bluntness and the incident shock position were varied. It is shown that the maximum Stanton number St _m in the shock incidence zone decreases with increase in the plate bluntness radius r to a certain value and then varies only slightly with further increase in r. In the case of a turbulent undisturbed boundary layer heat transfer is diminished with increase in r more slowly than in the case of a laminar undisturbed flow. In the presence of an incident shock the bluntness of the leading edge of the flat plate results in a greater decrease in the Stanton number than in the absence of the shock. With increase in the bluntness of the leading edge of the plate the separation zone first sharply lengthens and then decreases in size or remains constant.     

Pressure-Gradient Turbulent Boundary Layers Developing Around a Wing Section

A direct numerical simulation database of the flow around a NACA4412 wing section at R e _c = 400,000 and 5^° angle of attack (Hosseini et al. Int. J. Heat Fluid Flow 61, 117–128, 2016), obtained with the spectral-element code Nek5000, is analyzed. The Clauser pressure-gradient parameter β ranges from ? 0 and 85 on the suction side, and from 0 to ? 0.25 on the pressure side of the wing. The maximum R e _?? and R e _τ values are around 2,800 and 373 on the suction side, respectively, whereas on the pressure side these values are 818 and 346. Comparisons between the suction side with zero-pressure-gradient turbulent boundary layer data show larger values of the shape factor and a lower skin friction, both connected with the fact that the adverse pressure gradient present on the suction side of the wing increases the wall-normal convection. The adverse-pressure-gradient boundary layer also exhibits a more prominent wake region, the development of an outer peak in the Reynolds-stress tensor components, and increased production and dissipation across the boundary layer. All these effects are connected with the fact that the large-scale motions of the flow become relatively more intense due to the adverse pressure gradient, as apparent from spanwise premultiplied power-spectral density maps. The emergence of an outer spectral peak is observed at β values of around 4 for λ _z ? 0.65δ ₉₉, closer to the wall than the spectral outer peak observed in zero-pressure-gradient turbulent boundary layers at higher R e _?? . The effect of the slight favorable pressure gradient present on the pressure side of the wing is opposite the one of the adverse pressure gradient, leading to less energetic outer-layer structures.     

Flow visualization of supersonic laminar flow over a backward-facing step via NPLS

An experimental study on a supersonic laminar flow over a backward-facing step of 5 mm height was undertaken in a low-noise indraft wind tunnel. To investigate the fine structures of Ma = 3.0 and 3.8 laminar flow over a backward-facing step, nanotracer planar laser scattering was adopted for flow visualization. Flow structures, including supersonic laminar boundary layer, separation, reattachment, redeveloping turbulent boundary layer, expansion wave fan and reattachment shock, were revealed in the transient flow fields. In the Ma = 3.0 BFS (backward-facing step) flow, by measuring four typical regions, it could be found that the emergence of weak shock waves was related to the K–H (Kelvin–Helmholtz) vortex which appeared in the free shear layer and that the convergence of these waves into a reattachment shock was distinct. Based on large numbers of measurements, the structure of time-averaging flow field could be gained. Reattachment occurred at the location downstream from the step, about 7–7.5 h distance. After reattachment, the recovery boundary layer developed into turbulence quickly and its thickness increased at an angle of 4.6°. At the location of X = 14h, the redeveloping boundary layer was about ten times thicker than its original thickness, but it still had not changed into fully developed turbulence. However, in the Ma = 3.8 flow, the emergence of weak shock waves could be seen seldom, due to the decrease of expansion. The reattachment point was thought to be near X = 15h according to the averaging result. The reattachment shock was not legible, which meant the expansion and compression effects were not intensive.     

Effect of Flow Structures on Turbulence Statistics of Taylor-Couette Flow in the Torque Transition State

Direct numerical simulations of Taylor-Couette flow from Re= 8000 to 25000 have been conducted to investigate changes of turbulence statistics in the transition of the Reynolds number dependency of the mean torque near Re= 10000. The velocity fluctuations are decomposed into the contributions of the Taylor vortex and remaining turbulent fluctuations. Significant Reynolds number dependencies of these components are observed in the radial profiles of the Reynolds stress and the transmission of the mean torque. The contributions of Taylor vortex and turbulent components in the net amount of mean torque are evaluated. The Taylor vortex component is overtaken by the turbulent counterpart around Re= 15000 when they are defined as the azimuthally averaged component and the remnants. The results show that the torque transition can be explained by the competition between the contributions of azimuthally averaged Taylor vortex and the remaining turbulent components.     

Simulation of Receptivity and Induced Transition From Discrete Roughness Elements

Simulations have been carried out to predict the receptivity and growth of crossflow vortices created by Discrete Roughness Elements (DREs) The final transition to turbulence has also been examined, including the effect of DRE spacing and freestream turbulence. Measurements by Hunt and Saric (2011) of perturbation mode shape at various locations were used to validate the code in particular for the receptivity region. The WALE sub-grid stress (SGS) model was adopted for application to transitional flows, since it allows the SGS viscosity to vanish in laminar regions and in the innermost region of the boundary layer when transition begins. Simulations were carried out for two spanwise wavelengths: λ= 12mm (critical) and λ= 6mm (control) and for roughness heights (k) from 12 μm to 42 μm. The base flow considered was an ASU (67)-0315 aerofoil with 45 ⁰ sweep at -2.9 ⁰ incidence and with onset flow at a chord-based Reynolds number Re _c= 2.4x10 ⁶. For λ= 12mm results showed, in accord with the experimental data, that the disturbance amplitude growth rate was linear for k = 12 μm and 24 μm, but the growth rate was decreased for k = 36 μm Receptivity to λ= 6mm roughness showed equally good agreement with experiments, indicating that this mode disappeared after a short distance to be replaced by a critical wavelength mode. Analysis of the development of modal disturbance amplitudes with downstream distance showed regions of linear, non-linear, saturation, and secondary instability behaviour. Examination of breakdown to turbulence revealed two possible routes: the first was 2D-like transition (probably Tollmien-Schlichting waves even in the presence of crossflow vortices) when transition occurred beyond the pressure minimum; the second was a classical crossflow vortex secondary instability, leading to the formation of a turbulent wedge.     

Visualization of Supersonic Low-Noise Flow Over Surface-Mounted Two-Dimensional Prisms

An experimental study of supersonic flow over two-dimensional surface-mounted prisms is carried out in a Mach 3 low-noise wind tunnel. The noise level of this supersonic wind tunnel, defined as the root mean-square Pitot pressure fluctuation normalized by the mean Pitot pressure, can be reduced to about 0.37%. The nanotracer planar laser scattering (NPLS) technique is used to analyze the influence of the prism geometry and the oncoming flow conditions on the typical flow structures including separation and reattachment shocks. With increase in the prism height the induced shocks move upstream. At a constant streamwise length L of a prism the timeaveraged NPLS images show that the length of the downstream recirculation region increases from 0.8L to 1.2L, when the prism height H changes from 3 to 5 mm. As compared with the flow structures occurring downstream of the prisms, the upstream flow structures are more susceptible to the oncoming boundary layer and are considerably different in laminar and turbulent flows. The separation shock wave is clearly visible in turbulent flow even for the 1-mm prism, whereas in the case of laminar flow there is no a distinct shock wave upstream of this prism. At the same time, the location of the flow reattachment and the angle of the reattachment shock wave in the downstream flow remain almost the same in both two flow regimes.     

Effects of boundary layer on flame propagation generated by forced ignition behind an incident shock wave

To study the effects of the boundary layer on the deflagration to detonation transition (DDT) process, the mixture behind an incident shock wave was ignited using laser breakdown. Ignition timing was controlled so that the interaction of the resulting flame with a laminar or turbulent boundary layer could be examined. In the case of the interaction with a laminar boundary layer, wrinkling of the flame was observed after the flame reached the corner of the channel. On the other hand, interaction with the turbulent boundary layer distorted the flame front and increased the spreading rate of the flame followed by prompt DDT. The inner structure of the turbulent boundary layer plays an important role in the DDT process. The region that distorted the flame within the turbulent boundary layer was found to be the intermediate region \(0.01< y/\delta < 0.4\), where y is the distance from the wall and \(\delta \) is the boundary layer thickness. The flame disturbance by the turbulent motions is followed by the flame interaction with the inner layer near the wall, which in turn generates a secondary-ignition kernel that produced a spherical accelerating flame, which ultimately led to the onset of detonation. After the flame reached the intermediate region, the time required for DDT was independent of the ignition position. The effect of the boundary layer on the propagating flame, thus, became relatively small after the accelerating flame was generated.     

Plane acoustic wave propagation through a composite of elastic and Kelvin–Voigt viscoelastic material layers

The problem of plane wave propagation through a plane composite layer of thickness h is considered. The composite consists of periodically repeated elastic and Kelvin–Voigt viscoelastic material layers, and all layers are either parallel or perpendicular to the incident wave front. Moreover, it is assumed that the thickness of each separate layer of the composite is much less than the acoustic wave length and the thickness h of the entire composite. We study the problem by using a homogenized model of the composite, which allows us to find the reflection and transmission factors and the variation in the sound intensity level as it propagates though the composite layer of thickness h.     

Self-similar solutions in the problem of generalized vortex diffusion

The analysis of the group properties and the search for self-similar solutions in problems of mathematical physics and continuum mechanics have always been of interest, both theoretical and applied [1–3]. Self-similar solutions of parabolic problems that depend only on a variable of the type η = x/√t are classical fundamental solutions of the one-dimensional linear and nonlinear heat conduction equations describing numerous physical phenomena with initial discontinuities on the boundary [4]. In this study, the term “generalized vortex diffusion” is introduced in order to unify the different processes in mechanics modeled by these problems. Here, vortex layer diffusion and vortex filament diffusion in a Newtonian fluid [5] can serve as classical hydrodynamic examples. The cases of self-similarity with respect to the variable η are classified for fairly general kinematics of the processes, physical nonlinearities of the medium, and types of boundary conditions at the discontinuity points. The general initial and boundary value problem thus formulated is analyzed in detail for Newtonian and non-Newtonian power-law fluids and a medium similar in behavior to a rigid-ideally plastic body. New self-similar solutions for the shear stress are derived.     

Streamwise Vortices and Velocity Streaks in a Locally Drag-Reduced Turbulent Boundary Layer

This work aims to understand the changes associated with the near-wall streaky structures in a turbulent boundary layer (TBL) where the local skin-friction drag is substantially reduced. The Reynolds number is R e _?? = 1000 based on the momentum thickness or R e _τ = 440 based on the friction velocity of the uncontrolled flow. The TBL is perturbed via a local surface oscillation produced by an array of spanwise-aligned piezo-ceramic (PZT) actuators and measurements are made in two orthogonal planes using particle image velocimetry (PIV). Data analyses are conducted using the vortex detection, streaky structure identification, spatial correlation and proper orthogonal decomposition (POD) techniques. It is found that the streaky structures are greatly modified in the near-wall region. Firstly, the near-wall streamwise vortices are increased in number and swirling strength but decreased in size, and are associated with greatly altered velocity correlations. Secondly, the velocity streaks grow in number and strength but contract in width and spacing, exhibiting a regular spatial arrangement. Other aspects of the streaky structures are also characterized; they include the spanwise gradient of the longitudinal fluctuating velocity and both streamwise and spanwise integral length scales. The POD analysis indicates that the turbulent kinetic energy of the streaky structures is reduced. When possible, our results are compared with those obtained by other control techniques such as a spanwise-wall oscillation, a spanwise oscillatory Lorentz force and a transverse traveling wave.     

Imploding conical shock waves

The behaviour of conical shock waves imploding axisymmetrically was first studied numerically by Hornung (J Fluid Mech 409:1–12, 2000) and this prompted a limited experimental investigation into these complex flow patterns by Skews et al. (Shock Waves 11:323–326, 2002). Modification of the simulation boundary conditions, resulting in the loss of self-similarity, was necessary to image the flow experimentally. The current tests examine the temporal evolution of these flows utilising a converging conical gap of fixed width fed by a shock wave impinging at its entrance, supported by CFD simulations. The effects of gap thickness, angle and incident shock strength were investigated. The wave initially diffracts around the outer lip of the gap shedding a vortex which, for strong incident shock cases, can contain embedded shocks. The converging shock at exit reflects on the axis of symmetry with the reflected wave propagating outwards resulting in a triple point developing on the incident wave together with the associated shear layer. This axisymmetric shear layer rolls up into a mushroom-shaped toroidal vortex ring and forward-facing jet. For strong shocks, this deforms the Mach disk to the extent of forming a second triple point with the primary shock exhibiting a double bulge. Separate features resembling the Richtmeyer–Meshkov and Kelvin–Helmholtz instabilities were noted in some tests. Aside from the incident wave curvature, the reflection patterns demonstrated correspond well with the V- and DV-types identified by Hornung although type S was not clearly seen, possibly due to the occlusion of the reflection region by the outer diffraction vortex at these early times. Some additional computational work explicitly exploring the limits of the parameter space for such systems has demonstrated the existence of a possible further reflection type, called vN-type, which is similar to the von Neumann reflection for plane waves. It is recommended that the parameter space be more thoroughly explored experimentally.     

Application of unsteady mixing equations to some aerodynamic problems

Tangential discontinuities [1] are introduced in solving several transient and steady-state problems of gas dynamics. These discontinuities are unstable [2] as a result of the effects of viscosity and thermal conductivity. Therefore it is advisable to replace the tangential discontinuity by a mixing region and account for its interaction with the inviscid flows, establishing on the boundaries of this region the conditions of vanishing friction stress and equality of the velocity and temperature components to the corresponding velocity and temperature components of the inviscid flows. This formulation improves the accuracy of the solution of such problems by posing them as problems with irregular reflection and intersection of shock waves [1].The consideration of the interaction of unsteady turbulent mixing regions with the inviscid flow also permits the formulation of several problems in which the effects of viscosity lead to complete rearrangement of the flow pattern (the lambda-configuration) with the interaction of the reflected shock wave with the boundary layer in the shock tube [3,4], the formation of zones of developed separation ahead of obstacles, etc.).In this connection, §1 presents an analysis of the self-similar solutions of the unsteady turbulent mixing equations (a corresponding analysis of the laminar mixing equations which coincide with the boundary layer equations is presented in [1]). It is shown that these self-similar solutions describe, along with the several problems noted above, the problems of the formation of steady jets and mixing zones in the base wake.As an example, §2 presents, within the framework of the proposed schematization, an approximate solution of the problem of the interaction of a shock wave reflected from a semi-infinite wall with the boundary layer on a horizontal plate behind the incident shock wave. The results obtained are applied to the analysis of reflection in a shock tube. Computational results are presented which are in qualitative agreement with experiment [3, 4].     

可压缩流向涡与反向运动激波相互作用的实验

对可压缩流向涡与反向运动激波相互作用的现象进行了实验研究．实验在９４ｍｍ×９４ｍｍ的方截面激波管中进行．在实验段上游安装了一个有限翼展平直机翼．当入射激波通过机翼后，波后２区气流在模型翼尖诱导出一条流向涡．入射激波在激波管端壁反射后，形成的反射激波在观察窗处和流向涡发生作用．实验中拍摄了激波与流向涡作用全过程的纹影照片，观察到了一些和定常激波与旋涡相互作用不同的现象，并与数值计算结果进行了初步比较     

Assessment of Five SGS Models for Low-Rem MHD Turbulence

Assessment of three regularization-based and two eddy-viscosity-based subgrid-scale (SGS) turbulence models for large eddy simulations (LES) are carried out in the context of magnetohydrodynamic (MHD) decaying homogeneous turbulence (DHT) with a Taylor scale Reynolds number (Re_λ) of 120 and a MHD transition-to-turbulence Taylor-Green vortex (TGV) problems with a Reynolds number of 3000, through direct comparisons to direct numerical simulations (DNS). Simulations are conducted using the low-magnetic Reynolds number approximation (Re_m<<1). LES predictions using the regularization-based Leray- α,LANS- α, and Clark- α SGS models, along with the eddy viscosity-based non-dynamic Smagorinsky and the dynamic Smagorinsky models are compared to in-house DNS for DHT and previous results for TGV. With regard to the regularization models, this work represents their first application to MHD turbulence. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields made between the varying magnetic field cases demonstrated that the regularization models performed poorly compared to the eddy-viscosity models for all MHD cases, but the comparisons improved with increase in magnitude of magnetic field, due to a decrease in the population of SGS eddies within the flow field.     

Wind Impact on Single Vortices and Counterrotating Vortex Pairs in Ground Proximity

Wall-resolved large eddy simulations are employed to investigate the behaviour of wake vortices and single vortices in ground proximity at a variety of wind conditions. The six considered strengths of wind, ranging between 0.5 and 4 times the initial wake vortex descent speed, w₀, include practically and theoretically significant wind speeds. A crosswind of 0.5 w₀ may lead to windward stall posing a potential hazard to subsequently landing aircraft, whereas theoretical considerations predict that at 4 w₀ the rebound of the luff vortex is completely suppressed. The same range of wind speeds is also used to investigate the effects of headwind and diagonal wind in order to discriminate between effects of environmental turbulence increasing with wind speed and the direction of the wind shear. The study has been complemented by a number of single vortex computations in order to differentiate between effects related to the mutual interaction of the vortex pair and the individual vortices with the turbulent boundary layer flow. It is shown that vortex ascent, descent, rebound and decay characteristics are controlled by (i) the interaction of the vortices with secondary vorticity detaching from the ground, (ii) the redistribution of vorticity of the boundary layer which is altering the path of the primary vortices by mutual velocity induction, and (iii) the interaction of the vortices with the environmental turbulence.     

Large Eddy Simulation of Compressible Subsonic Turbulent Jet Starting From a Smooth Contraction Nozzle

Compressible subsonic turbulent starting jet with a relatively large Reynolds number of significant practical importance is investigated using large eddy simulation (LES), starting from a smooth contraction nozzle. The computational domain of truncated conical shape is determined through the comparison of the time-averaged numerical solution with the particle imaging velocimetry measurements for the steady jet. It is shown that the starting jet consists of a leading vortex ring followed by a quasi-steady jet, and the instantaneous velocity field exhibits contraction and expansion zones, corresponding to the high pressure (HP) and low pressure (LP) regions formed by the convecting vortex rings, and are related to the Kelvin-Helmholtz instability. The thin boundary layer inside the smooth contraction nozzle evolves into a shear layer at the nozzle exit and develops with the downstream penetration of the jet. Using λ ₂ criterion, the formation and evolution of the vortical structures are temporally visualized, illustrating distortion of vortex rings into lobed shapes prior to break-down. Rib-shape streamwise vortex filaments exist in the braid region between a pair of consecutive vortex rings due to secondary instabilities. Finally, formation and dynamics of hairpin vortices in the shear layer is identified.     

Kovasznay Mode Decomposition of Velocity-Temperature Correlation in Canonical Shock-Turbulence Interaction

The correlation coefficient R_uT between the streamwise velocity and temperature is investigated for the case of canonical shock-turbulence interaction, motivated by the fact that this correlation is an important component in compressible turbulence models. The variation of R_uT with the Mach number, the turbulent Mach number, and the Reynolds number is predicted using linear inviscid theory and compared to data from DNS. The contributions from the individual Kovasznay modes are quantified. At low Mach numbers, the peak post-shock R_uT is determined by the acoustic mode, which is correctly predicted by the linear theory. At high Mach numbers, it is determined primarily by the vorticity and entropy modes, which are strongly affected by nonlinear and viscous effects, and thus less well predicted by the linear theory.     

Turbulent Drag Reduction by a Near Wall Surface Tension Active Interface

In this work we study the turbulence modulation in a viscosity-stratified two-phase flow using Direct Numerical Simulation (DNS) of turbulence and the Phase Field Method (PFM) to simulate the interfacial phenomena. Specifically we consider the case of two immiscible fluid layers driven in a closed rectangular channel by an imposed mean pressure gradient. The present problem, which may mimic the behaviour of an oil flowing under a thin layer of different oil, thickness ratio h₂/h₁ =?9, is described by three main flow parameters: the shear Reynolds number Re _τ (which quantifies the importance of inertia compared to viscous effects), the Weber number We (which quantifies surface tension effects) and the viscosity ratio λ = ν₁/ν₂ between the two fluids. For this first study, the density ratio of the two fluid layers is the same (ρ₂ = ρ₁), we keep Re _τ and We constant, but we consider three different values for the viscosity ratio: λ =?1, λ =?0.875 and λ =?0.75. Compared to a single phase flow at the same shear Reynolds number (Re _τ =?100), in the two phase flow case we observe a decrease of the wall-shear stress and a strong turbulence modulation in particular in the proximity of the interface. Interestingly, we observe that the modulation of turbulence by the liquid-liquid interface extends up to the top wall (i.e. the closest to the interface) and produces local shear stress inversions and flow recirculation regions. The observed results depend primarily on the interface deformability and on the viscosity ratio between the two fluids (λ).