Formation Of Hairpin Vortices Research Articles

Effect of stratification on the propagation of a cylindrical gravity current

Direct numerical simulations (DNSs) of three-dimensional cylindrical release gravity currents in a linearly stratified ambient are presented. The simulations cover a range of stratification strengths $0< S\leq 0.8$ (where $S=(\rho _b^*-\rho _0^*)/(\rho _c^*-\rho _0^*), \rho _b^*, \rho _0^*$ and $\rho _c^*$ are the dimensional density at the bottom of the domain, top of the domain and the dense fluid, respectively) at two different Reynolds numbers. A comparison between the stratified and unstratified cases illustrates the influence of stratification strength on the dynamics of cylindrical gravity currents. Specifically, the front velocity in the slumping phase decreases with increasing stratification strength whereas the duration of the slumping phase increases with increments of $S$ . The Froude number calculated in this phase shows a good agreement with models proposed by Ungarish & Huppert (J. Fluid Mech., vol. 458, 2002, pp. 283–301) and Ungarish (J. Fluid Mech., vol. 548, 2006, pp. 49–68), originally developed for planar gravity currents in a stratified ambient. In the inertial phase, the front velocity across cases with different stratification strengths adheres to a power-law scaling with an exponent of $-$ 1/2. Higher Reynolds numbers led to more frequent lobe splitting and merging, with lobe size diminishing as stratification strength increased. Strong interactions among inner vortex rings occurred during the slumping phase, leading to the early formation of hairpin vortices in weakly stratified cases, while strongly stratified cases exhibited delayed vortex formation and less turbulence.

Tip effects on three-dimensional flow structures over low-aspect-ratio plates: mechanisms of spanwise fluid transport

Three-dimensional flows over low-aspect-ratio rectangular flat plates ( ${A{\kern-4pt}R} = 1.00$ – $1.50$ ) are investigated using tomographic and planar particle image velocimetry techniques. The chord-based Reynolds number is $5400$ , and the angle of attack is fixed at $6^\circ$ . This study reveals for the first time the interplay between spanwise fluid transport and downwash, both originating from the tip effects. Spanwise fluid transport promotes the formation and subsequent coherent development of leading-edge vortices, whereas downwash stabilizes the flow. Specifically, two mechanisms related to spanwise fluid transport are revealed. First, the spanwise fluid transport enhances the intensity of the reversed flow, promoting the shear layer roll-up and vortex shedding. Second, the near-wall spanwise flow interacts with the shed C-shape vortices, thereby strengthening the vortex heads. In particular, through these interactions, spanwise fluid transport can sustain the coherence of the C-shape vortices until the vortex heads split in a regular fashion. Consequently, the C-shape vortices are transformed into novel Þ-shape vortices for the plates of ${A{\kern-4pt}R} \leq 1.25$ , which supplements the previously discovered transformation from C-shape to M-shape vortices for larger ${A{\kern-4pt}R}$ plates. Downstream of this novel vortex-splitting transformation, two fundamental processes contribute to the formation of hairpin vortices. The above comprehensive understanding of complete vortex evolution routine provides valuable insights into the tip effects on the formation of three-dimensional flows over low- ${A{\kern-4pt}R}$ plates.

Tomographic PIV investigation on near-wake structures of a hemisphere immersed in a laminar boundary layer

The near wake of a hemisphere immersed in a laminar boundary layer is studied utilizing time-resolved tomographic particle image velocimetry (TPIV). Focus is placed on the three-dimensional vortical structures and the formation details of hairpin vortices before the onset of transition. The three-dimensional instantaneous pressure field of the hemisphere wake is reconstructed for better understanding the flow mechanism. Experiments are carried out with Reynolds number $Re_{r}=1370$ , based on the hemisphere radius $R$ . Features of periodicity of the near wake are analysed using proper orthogonal decomposition and Fourier transformation. The velocity fluctuation in the wall-normal direction is shown to be crucial to the formation of hairpin vortices in the near wake. By investigating the transport of mass and vorticity, and the correlation between pressure and hairpin vortex strength, the formation mechanism is revealed clearly. Specifically, the main hairpin vortices (MHVs) are formed within the reaction of outer high-speed flow and near-wall flow. The formation of the head portion is followed by the leg portion formation. The shedding of the MHVs is highly correlated with the pressure, as well as the pressure gradient in the wall-normal direction. For the side hairpin vortices (SHVs), the leg portion is formed first, followed by the generation of the head portion thanks to induction of the re-oriented standing vortices. The generation of the SHVs can be regarded as the downstream bridging of the standing vortices, similar to the generation of hairpin vortices due to the connection of streamwise vortices in turbulent boundary layers.

Flow Separation in Airfoils with Rough Leading Edges

In this study we consider the flow over airfoils with leading-edge roughness, designed to mimic the ice depositions that may occur on an aircraft in flight. The focus of this investigation is the effect of the angle of attack on the mean-flow three-dimensionality. In our previous work (Kumar et al., Journal of Turbulence, Vol. 22, No. 11, 2021, pp. 735–760), we found stationary spanwise inhomogeneities in the form of alternating regions of fast- and slow-moving fluid, which were termed “flow channels.” In the present study we investigate further this phenomenon. We observe the formation of hairpin vortices downstream of the roughness elements, which eventually merge; this causes the formation of wider channels that remain coherent and affect the trailing-edge separation. With increasing angle of attack, the intensity of flow channeling can increase or decrease depending on the topology of the leading-edge roughness. Its effect on the trailing-edge separation remains, however, significant. The mean-separation line is highly distorted, and the separation length can vary by up to 30% of the chord length along the span.

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Global stability analysis and direct numerical simulation (DNS) are used to study boundary layer flows with an isolated roughness element. The aspect ratio of the element ( $\eta$ ) is small, while the ratio of element height to displacement boundary layer thickness ( $h/\delta ^{*}$ ) is large. Both steady base flows and time-averaged mean flows are able to capture the frequencies of the primary vortical structures and mode shapes. Global stability results highlight that although the varicose instability is dominant for large $h/\delta ^{*}$ , sinuous instability becomes more pronounced as $Re_h$ increases for the thin geometry ( $\eta =0.5$ ), due to increased spanwise shear in the near-wake region. Wavemaker results indicate that $\eta$ affects the convective nature of the shear layer more than the type of instability. DNS results show that different instability mechanisms lead to different development and evolution of vortical structures in the transition process. For $\eta =1$ , the varicose instability is associated with the periodic shedding of hairpin vortices, and its stronger spatial transient growth indicated by wavemaker results aids the formation of hairpin vortices farther downstream. In contrast, for $\eta =0.5$ , the interplay between varicose and sinuous instabilities results in a broader-banded energy spectrum and leads to the sinuous wiggling of hairpin vortices in the near wake when $Re_h$ is sufficiently high. A sinuous mode with a lower frequency captured by dynamic mode decomposition analysis, and associated with the ‘wiggling’ of streaks, persists far downstream and promotes transition to turbulence. A new regime map is developed to classify and predict instability mechanisms based on $Re_{hh}^{1/2}$ and $d/\delta ^{*}$ using a logistic regression model. Although the mean skin friction demonstrates different evolutions for the two geometries, both of them efficiently trip the flow to turbulence at $Re_h=1100$ . An earlier location of a fully-developed turbulent state is established for $\eta =1$ at $x \approx 110h$ .

Numerical Prediction of Turbulent Drag Reduction with Different Solid Fractions and Distribution Shapes over Superhydrophobic Surfaces

The exploration of superhydrophobic drag reduction has been and continues to be of significant interest to various industries. In the present work, direct numerical simulation (DNS) is utilized to investigate the effect of the parameters on the drag-reducing performance of superhydrophobic surfaces (SHS). Simulations with a friction Reynolds number of 180 were carried out at solid fraction values of ϕs=116,111, and 14, and three distribution shapes: aligned, staggered, and random. The top wall is the smooth one, and the bottom wall is a superhydrophobic surface (SHS). Drag reduction and Reynolds stress profiles are compared for all cases. The turbulent kinetic energy budget, including production, dissipation, and diffusion, is presented with respect to the solid fraction and type of distribution to investigate the drag reduction mechanism. The sizes of the longitudinal vortices and formation of hairpin vortices are investigated through the observation of coherent structures. The simulation of a post model is a useful method to study the drag reduction for different solid fraction values and distribution geometries. Our study demonstrates that the drag reduction could acquire 42% with the solid fraction value ϕs=116 and an aligned distribution shape for post superhydrophobic surface geometry. Our study also showed the relationship of the Reynolds stress component (R11, R22, and R33) to the drag reduction with the differences in the solid fraction values and distribution geometry. In which, the R11 component has the most change between an aligned distribution and a random one. The peak value of R11 tends to shift away from the SHS wall. In addition, the analysis of the TKE budget over the superhydrophobic surface was performed, which can be adopted as a useful resource in turbulence modeling based on RANS methodology.

Dynamics of the interaction of synthetic jet vortex rings with a stratified interface

The vortex dynamics in a stratified environment is of fundamental importance in various flow systems, however, the mechanism of successive vortex–interface interactions remains not fully understood. This study investigates synthetic jet vortex rings impinging on a water–oil interface by experiment and numerical simulation. Two cases in the laminar and transitional regimes are concerned with the Froude number (Fr) of 0.35 and 0.82, respectively. The vortex rings for the two cases follow a similar evolution with three distinct stages, including vortex free-travel, vortex–interface interaction and vortex stretching. As products of the vortex–interface interaction, the secondary vortex rings are baroclinically generated in both water and oil followed by the formation of hairpin vortices through azimuthal deformation. Distinguished from an isolated vortex–interface interaction, complex interactions occur between the primary vortex ring and hairpin vortices, which can enhance the vortex ring instability in existence of the stratification for the laminar case. However, the vortex ring instability for the transitional case can develop earlier due to nonlinear effects with increasing Reynolds number. The spatio-temporal properties of the interface deformation and interfacial waves are analysed. The maximum penetration height of vortex rings scales with Fr2 as that for the isolated situation. Particularly, the transitional case is found to produce destabilization of the interfacial waves at a further radial location. The mechanism is revealed by connecting the dynamics of the vortex and the interface, which can be attributed to the radial development of perturbances stemming from the vortex ring instability under strong vortex–interface interaction.

Laminar forced convection heat transfer around wavy elliptic cylinders with different aspect ratios

The present study investigates the forced convection heat transfer around the wavy elliptic cylinders by considering wide range of wavelength (λ) for different aspect ratios (AR). The wake thermal structures were classified into four modes of the quasi-2D unsteady, quasi-2D steady, complex 3D unsteady and 3D steady structures, which is mapped in AR-λ plane. The short wavelengths formed the quasi-2D thermal structure for both steady and unsteady forced convections. The quasi-2D unsteady structure is characterized by the spanwise nearly invariant isothermal structures and the periodical time evolution of the Nusselt number. The long wavelengths formed the 3D thermal structure in the present range of AR. The complex 3D unsteady thermal structure is featured by the hole and spanwise separated formation of the temperature iso-surface owing to the vortex dislocation and hairpin vortex formation. The 3D steady thermal structure also appeared in the steady regime and the spanwise dependence of the thermal structure became considerable with decreasing AR. The surface distribution of the mean Nusselt number depended on the regime of the thermal structures. In the long wavelength region, the additional appearance of two types of the streamwise vorticities locally attenuated the heat transfer by weakening the reverse flow in the near wake. As the cylinder becomes more elliptic, the two types of the streamwise vorticities becomes weak and finally disappears, resulting in weakening the effect of the local attenuation of the heat transfer. Therefore, it can be concluded that the streamlined shape is predominant to the stabilization of the forced convection with decreasing AR, regardless of the wavelength .

Slat cove dynamics of low Reynolds number flow past a 30P30N high lift configuration

A three-dimensional computational fluid dynamics analysis of low Reynolds number [O(104)] flow over a 30P30N three-element high lift wing is carried out using a high-order spectral element method. In this article, we study the flow in the slat cove region and the slat wake/shear layer interaction. Vortical structures, identified in the computations, are very similar to those visualized in recent experiments. For Reynolds numbers below a critical interval (found in recent experiments), Görtler vortices are observed in the slat wake, while for Reynolds numbers above the critical interval, a roll-up is observed in the slat cove and both streamwise and spanwise vortices form in the slat wake. Prior to the formation of Görtler and roll-up vortices, three-dimensional tongue- or rib-like vortex shapes, similar to those found in the wake of bluff bodies, are observed in the slat cove and promote transition to three-dimensional flow. Above the critical interval, streaks and spanwise vortices are observed to dominate the slat wake and lead to the formation of hairpin vortices which contribute to the transition to turbulence. Integral flow parameters such as lift, drag, and pressure coefficients are analyzed in the range of Reynolds numbers studied.

Inner structures of Görtler streaks

The hypersonic boundary layer transition over a concave wall is investigated in a Mach 6.5 quiet wind tunnel using temperature sensitive paint (TSP), CO2-enhanced filtered Rayleigh scattering flow visualization, PCB fast-response pressure sensors, and a high-frequency schlieren technique. The TSP shows that low- and high-temperature streaks are distributed in the spanwise direction. The wavelengths of naturally developing Görtler streaks are randomly distributed, with an average of approximately 7 mm, and change little as the unit Reynolds number increases. More importantly, three-dimensional waves are clearly visualized and quantitatively measured inside the Görtler streaks. This is the first time that the entire evolution of the Görtler instability has been visualized using the Rayleigh-scattering flow visualization in hypersonic flow. The results demonstrate that three-dimensional waves are amplified as a result of the Görtler instability, resulting in a localized high-shear layer around the interface of the three-dimensional waves, which contributes to the formation of hairpin vortices and mushroom-like structures. The three-dimensional waves grow and play an important role in Görtler instability-induced boundary layer transitions.

Liutex core line and POD analysis on hairpin vortex formation in natural flow transition

In this study, the new method of the vortex core line based on Liutex definition, also known as Liutex core line, is applied to support the hypothesis that the vortex ring is not a part of the Λ - vortex and the formation of the ring-like vortex is formed separately from the Λ - vortex. The proper orthogonal decomposition (POD) is also applied to analyze the Kelvin-VHelmholtz (K-H) instability happening in hairpin ring areas of the flow transition on the flat plate to understand the mechanism of the ring-like vortex formation. The new vortex identification method named modified Liutex-Omega method is efficiently used to visualize and observe the shapes of vortex structures in 3-D. The streamwise vortex structure characteristics can be found in POD mode one as the mean flow. The other POD modes are in stremwise and spanwise structures and have the fluctuation motions, which are induced by K-H instability. Moreover, the result shows that POD modes are in pairs and share the same characteristics such as amplitudes, mode shapes, and time evolutions. The vortex core and POD results confirm that the Λ - vortex is not self-deformed to a hairpin vortex, but the hairpin vortex is formed by the K-H instability during the development of Lambda vortex to hairpin vortex in the boundary layer flow transition.

Dynamics of bubbles rising in pseudo-2D bubble column: Effect of confinement and inertia

2D Rectangular columns, formed within a thin gap between two enclosed parallel plates, are often used in visualisation and CFD studies of multiphase flows. In this study, a numerical analysis is performed on the dynamics of a bubble rising in such setup (D = 5–7 mm, Re ≈ 1000–2000), with the aim of determining the effect of the size of the gap (h) on the velocity field around it. For most cases, the bubble adopts an oblate spheroidal shape, with chaotic rise behaviour and continual fluctuations in both aspect ratio, orientation, and velocity. The bubble aspect ratio generally decreases with increasing level of confinement, because of increased level of resistance provided by the walls. With increasing Reynolds number, however, the bubble (D = 7 mm, h/D = 1) is found to display a more elongated oblate spheroidal shape and a rise behaviour that is largely rectilinear. This change in behaviour has been attributed towards severe disruptions in the development of toroidal vortex formation at the walls, confining the formation of hairpin vortices towards the side interface of the bubble at the centreline of the column. This prevents the development of large-scale fluctuations and confines the path oscillation of the bubble towards high-frequency fluctuations. Further, the formation of a region of recirculating flow is also evident, as a result of rapid detachment of vortices at the bubble equator. Intense fluctuation in velocity in the horizontal direction parallel to the wall is developed, and the dissipation in this fluctuation, as well as in the time-averaged velocity below the bubble, is found to occur more gradually than in the case of columns with larger gaps.

Vortex Structure Analysis of Grooved Surface Flow Loss

Large eddy simulations were used to study the effect of groove structures on rotational motion of fluid in wall turbulence, from the perspective of coherent structures. The results show that groove structures reduce the per unit normal height internal velocity gradient in the near-wall region and decrease shear stress and viscous resistance. Concurrently, owing to the decrease in the velocity gradient, shear action is weakened, and the vortices’ level of stretch is reduced in the near-wall region of the grooved surface. The groove structures change the distribution of the shear layers in the boundary layer and increase the stability of the strips. The reduction of spanwise vorticities delayed the formation of hairpin vortices caused by the instability of strips and so on; and the energy dissipation is effectively reduced in the flow process.

Characterizing the formation and regeneration of hairpin vortices in a laminar boundary layer

A free surface water channel is used to study hairpin vortex formation created by fluid injection through a narrow slot into a laminar boundary layer. Particle image velocimetry flow-field measurements of injections into quiescent cross-flow conditions confirm that elongated ring vortices are produced with a nondimensionalized circulation strength that is approximately linear with formation time. Unlike circular ring vortices, a limiting strength is not observed at a nondimensional formation time of 4 due to the proximity of the counter-rotating vortex pair. Identical injections are made into a laminar boundary layer at different free-stream velocities and streamwise slot positions (485 ≤ Reδ∗ ≤ 584) with average injection velocity ratios between 0.08 and 0.16. Visualizations indicate that the shear layer between the low x-momentum injected fluid and the boundary layer creates a Kelvin-Helmholtz instability that forms the hairpin vortex head which then monotonically decreases in circulation strength with downstream distance. A similar process can form, or regenerate, a secondary hairpin vortex upstream of the primary vortex with a circulation strength of the head that is comparable to the strength of the primary head at the time of regeneration. However, the legs of the primary vortex continue to strengthen up to regeneration. The peak circulation in the legs is not directly correlated to the strength of the original elongated ring vortex. However, when the circulation is scaled with the injection momentum ratio it is linearly related to scaled injection time. It is proposed that the injection momentum ratio and nondimensionalized injection time based on the wall normal penetration time can be used to identify threshold conditions which produce a secondary vortex. It is suggested that this criterion may be used to identify the minimum strength of flow structures that would be capable of regeneration and thus transition initiation.

Cavitation about a jet in crossflow

Cavitation occurrence about a jet in crossflow is investigated experimentally in a variable-pressure water tunnel using still and high-speed photography. The 0.012 m diameter jet is injected on the centreplane of a 0.6 m square test section at jet to freestream velocity ratios ranging from 0.2 to 1.6, corresponding to jet-velocity-based Reynolds numbers of$25\times 10^{3}$to$160\times 10^{3}$respectively. Measurements were made at a fixed freestream-based Reynolds number, for which the ratio of the undisturbed boundary layer thickness to jet diameter is 1.18. The cavitation number was varied from inception (up to about 10) down to 0.1. Inception is investigated acoustically for bounding cases of high and low susceptibility to phase change. The influence of velocity ratio and cavitation number on cavity topology and geometry are quantified from the photography. High-speed photographic recordings made at 6 kHz provide insight into cavity dynamics, and derived time series of spatially averaged pixel intensities enable frequency analysis of coherent phenomena. Cavitation inception was found to occur in the high-shear regions either side of the exiting jet and to be of an intermittent nature, increasing in occurrence and duration from 0 to 100 % probability with decreasing cavitation number or increasing jet to freestream velocity ratio. The frequency and duration of individual events strongly depends on the cavitation nuclei supply within the approaching boundary layer. Macroscopic cavitation develops downstream of the jet with reduction of the cavitation number beyond inception, the length of which has a power-law dependence on the cavitation number and a linear dependence on the jet to freestream velocity ratio. The cavity closure develops a re-entrant jet with increase in length forming a standing wave within the cavity. For sufficiently low cavitation numbers the projection of the re-entrant jet fluid no longer reaches the cavity leading edge, analogous to supercavitation forming about solid cavitators. Hairpin-shaped vortices are coherently shed from the cavity closure via mechanisms of shear-layer roll-up similar to those shed from protuberances and jets in crossflow in single-phase flows. These vortices are shed at an apparently constant frequency, independent of the jet to freestream velocity ratio but decreasing in frequency with reducing cavitation number and cavity volume growth. Highly coherent cavitating vortices form along the leading part of the cavity due to instability of the jet upstream shear layer for jet to freestream velocity ratios greater than about 0.8. These vortices are cancelled and condense as they approach the trailing edge in the shear layer of opposing vorticity associated with the cavity closure and the hairpin vortex formation. For lower velocity ratios, where there is decreased jet penetration, the jet upstream shear velocity gradient reverses and vortices of the opposite sense form, randomly modulated by boundary layer turbulence.

Three-dimensional laryngeal flow fields induced by a model vocal fold polyp

Pathological laryngeal flow fields are investigated in a dynamically-driven, scaled-up model of the vocal folds. Disruption of the flow field due to the presence of a geometric protuberance, representative of a sessile unilateral polyp, is investigated in both the streamwise and transverse flow directions using phase-averaged particle image velocimetry. It is shown that the protuberance disrupts the normal flow behavior of the glottal jet throughout the phonatory cycle. During the divergent portions of the glottal cycle, the flow is characterized by the formation of hairpin vortices downstream of the protuberance. The protuberance also introduces significant velocity gradients in the anterior-posterior direction, which cover ∼30−40% of the vocal fold length. It is proposed that the disruption of the normal velocity behavior owing to the presence of a polyp will adversely impact the aerodynamic loadings that drive vocal fold motion, contributing to the temporal and spatial vocal fold asymmetries that are clinically-observed in patients with unilateral polyps.

Turbulent Flow Separation Control over a Two-Dimensional Ramp Using Synthetic Jets

An experiment study of flow control using an array of three circular synthetic jets has been carried out in a separated turbulent flow over a two-dimensional ramp in a boundary-layer tunnel. The freestream velocity is 6:5 m=s and the Reynolds number based on the momentum thickness at a reference location upstream of the synthetic jet array is Re 1150. The synthetic array is operated at mean jet-to-freestream velocity ratios ranging from 0.2 to 0.5 and a reduced frequency based on the ramp height of F 0:2 and 0.6. Two-dimensional particle image velocimetry is employed to evaluate the control effect of synthetic jets at different actuator operating conditions in both timeand phase-averaged senses. Stereo particle image velocimetry is used to reveal the vortical structures thatwere responsible for theflow separation delay. It is found that at both reduced frequencies an increase in velocity ratio results in a further reduction in the height of the reverse-flow region, and somedifferences exist in the way inwhich the reverseflowresponds to jet actuation of the twodifferent reduced frequencies. It is also found that at the conditions tested in the present study, the interaction of synthetic jets with the turbulent boundary layer results in formation of hairpin vortices, which induce a further pair of streamwise vortices of the opposite sign of rotation directly underneath. It is believed that it is the streamwise vortices that produce a downwash bringing highmomentum fluid toward the wall, hence reducing the flow separation.

Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle

Large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted. The fully compressible Favre-filtered Navier–Stokes equations are coupled with a homogeneous equilibrium cavitation model. The dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms. The equations are numerically integrated in the context of a generalized curvilinear coordinate system to facilitate geometric complexities. A sixth-order compact finite difference scheme is employed for the Navier–Stokes equations with the AUSM+-up scheme to handle convective terms in the presence of large density gradients. The stiffness of the system due to the incompressibility of the liquid phase is addressed through an artificial increase in the Mach number. The simulation predicts the formation of a vapor cavity at the venturi throat with an irregular shedding of the small scale vapor structures near the turbulent cavity closure region. The vapor formation at the throat is observed to suppress the velocity fluctuations due to turbulence. The collapse of the vapor structures in the downstream region is a major source of vorticity production, resulting into formation of hair-pin vortices. A detailed analysis of the vorticity transport equation shows a decrease in the vortex-stretching term due to cavitation. A substantial increase in the baroclinic torque is observed in the regions where the vapor structures collapse. A spectra of the pressure fluctuations in the far-field downstream region show an increase in the acoustic noise at high frequencies due to cavitation.

Compressibility Effects on Boundary-Layer Transition Induced by an Isolated Roughness Element

Direct numerical simulation has been used to study the transition to turbulence of a high-speed boundary layer over a flat plate with an isolated roughness element. The roughness element consists of a continuous bump that is approximately half the boundary-layer thickness in height. Simulations at Mach 3 and Mach 6 have been run over a range of Reynolds numbers for two fixed wall temperatures corresponding to either an adiabatic or a cooled wall condition. In each case a lift-up of low momentum fluid away from the wall is observed leading to the formation of a detached shear layer. Acoustic disturbances are imposed to stimulate the instability of this layer and breakdown to turbulence is observed in the simulations at the highest Reynolds number in all cases except for the Mach 6 cold wall condition. The magnitude of the streamwise vorticity behind the roughness element increases with roughness height Reynolds number and is relatively insensitive to Mach number and wall temperature. Strouhal numbers associated with hairpin vortex formation are generally lower than in incompressible flow. The critical roughness height Reynolds number for transition within the computational domain is found to increase as the Mach number increases and is higher for the cooled wall condition. A correlation based on roughness height Reynolds and Mach numbers and wall temperature is found to separate laminar from transitional cases for the range of flow conditions studied.

Direct numerical simulations of localized disturbances in pipe Poiseuille flow

We consider pipe Poiseuille flow subjected to a disturbance which is highly localized in space. Experiments by Peixinho and Mullin have shown this disturbance to be efficient in triggering turbulence, yielding a threshold dependence on the required amplitude as R - 1.5 on the Reynolds number, R. The experiments also indicate an initial formation of hairpin vortices, with each hairpin having a length of approximately one pipe radius, independent of the Reynolds number in the range of R = 2000 – 3000 . We perform direct numerical simulations for R = 5000 . The results show a packet of hairpin vortices traveling downstream, each having a length of approximately one pipe radius. The perturbation remains highly localized in space while being advected downstream for approximately 10 pipe diameters. Beyond that distance from the disturbance origin, the flow becomes severely disordered.