Local Boundary Layer Thickness Research Articles

Turbulent activity in the near-wall region of adverse pressure gradient turbulent boundary layers

Two direct numerical simulation (DNS) databases are investigated to understand the effect of the outer-layer turbulence on the inner layer’s structures and energy transfer mechanisms. The first DNS database is the non-equilibrium adverse-pressure-gradient (APG) turbulence boundary layer (TBL) of Gungor et al. [1]. Its Reynolds number and the inner-layer pressure gradient parameter reach above 8000 and 10, respectively. The shape factor spans between 1.4 and 3.3, which indicates the flow has various velocity defect situations. The second database is the same flow as the first one but the outer layer turbulence is artificially eliminated in this flow. Turbulence is removed above 0.15 local boundary layer thickness. For the analysis, we chose four streamwise positions with small, moderate, large, and very-large velocity defect. We compare the wall-normal distribution of Reynolds stresses, two-point correlations and spectral distributions of energy, production and pressure strain. The results show that the inner layer turbulence can sustain itself when the outer-layer turbulence does not exist regardless of the velocity defect or the pressure gradient. The two-point correlations of both cases show that outer large-scale structures affect the inner layer structures significantly. The streamwise extent of the correlation contours scales with pressure-viscous units. This shows the importance of the pressure gradient’s effect on the inner-layer structures. The spectral distributions demonstrate that the energy transfer mechanisms are probably the same in the inner layer regardless of the velocity defect, which suggests the near-wall cycle may exist even in very-large defect APG TBLs where the mean shear in the inner layer is considerably lower than small-defect APG TBLs.

Experimental investigation of hypersonic boundary layer instability with wavy wall located downstream of synchronization point

The wavy wall surface has been reported to be effective in suppressing the growth of second mode instability waves in hypersonic boundary layer, while the allocation of wavy wall relative to the synchronization point requires further study. Upon this work experimental investigation of hypersonic boundary layer instability with wavy wall located downstream of synchronization point based on 7° half-angle sharp cone at zero angle of attack was carried out in a hypersonic noisy wind tunnel. The evolution of instability waves with wavy wall surface is measured using both surface-mounted pressure fluctuation sensors and focused laser differential interferometer (FLDI). The results reveal that the growth of instability waves has been enhanced significantly when the wavy wall region is allocated downstream of the synchronization point when the wavy wall height is slightly smaller than the local boundary layer thickness. Additionally, second mode instability waves are observed at both crests and troughs within the wavy wall region based on the FLDI measurement and moreover, the high-frequency instability waves measured in the separation bubbles of troughs are speculated to be the transmission of second mode instability waves from the shear layer, rather than the local generation of second mode instability.

Response of second-mode instability to backward-facing steps in a high-speed flow

Stability in a Mach 4.5 boundary layer over backward-facing steps (BFSs) is investigated using numerical methods. Two types of cases are considered with different laminar inflow conditions, imposed with single-frequency or broadband-frequency modes, respectively. Compared with the typical K-type transition over a flat plate, the boundary layer transition initiated by 90 kHz-frequency second mode appears to follow the same pattern but with a noticeable delay over the step. A larger step height leads to a better inhibition of the downstream Λ-vortices and thus a later transition, providing the step height is smaller than the local boundary layer thickness. Moreover, both the frequency weighted power spectral density and the root mean square of the streamwise velocity indicate the presence of Kelvin–Helmholtz (K–H) instability when the step height is equivalent to the thickness of the nearby boundary layer. There may exist an optimal step height for suppressing single-frequency (90 kHz) mode without exciting significant K–H modes. Similar to the previous studies on roughness, BFS can act as an amplifier for the low-frequency second modes and a suppressor for the high-frequency second modes. The critical frequency is equal to that of the unstable mode whose synchronization point is exactly located at the step corner. Additionally, the correction effects of the step induce the change of the phase speed of the fast mode, which correspondingly results in the movement of the synchronization point. Generally, the BFS is not able to completely alleviate the transition initiated by the broadband-frequency second modes but can still delay the boundary layer transition in a certain degree by suppressing the high-frequency unstable waves.

Passive flow control for the E423 airfoil utilizing an equilateral triangular trip

A passive flow control technique of utilizing an equilateral triangular trip close to the leading edge was developed and tested for a micro-scale Eppler E423 airfoil at a Reynolds number based on the chord of 40 000. The analysis was carried out via high-order wall-resolved large eddy simulation using the computational solver HpMusic. Angles of attack of 5° and 20° were tested. It was shown that at an angle of attack of 5°, the trip height of two times the local boundary layer thickness outperformed existing passive flow control techniques from the literature by almost a factor of five in terms of the lift-to-drag ratio. To understand the underlying physics which allowed the trip to provide this very significant performance benefit, metrics such as pressure coefficient profiles, oil flows, iso-surfaces of Q-criteria, and leading-edge flow behavior were examined. It was found that this trip configuration simultaneously removed the flow separation regions on both the suction and pressure sides of the wing.

Impact of compliant coating on Mack-mode evolution in hypersonic boundary layers

This paper focuses on the linear evolution of Mack instability modes in a hypersonic boundary layer over a flat plate that is partially coated by a compliant section. The compliant section is a thin, flexible membrane covering on a porous wall consisting of micro holes. The instability pressure could induce a vibration of the membrane, leading to a feedback to the boundary-layer fluids through the transverse velocity fluctuation. Such a process is formulated by an admittance boundary condition for the boundary-layer perturbation, which is dependent on the thickness and tension of the membrane, the properties of the porous wall, and the frequency of the Mack-mode perturbation. Using this admittance condition, the impact of the compliant coating on the Mack growth rate is studied systematically by solving the compressible Orr–Sommerfeld equations. It is found that the compliant coating could suppress the Mack instability with a frequency band in the neighbourhood of the most unstable frequency, and the stabilising frequency band widens as the membrane thickness and tension decrease, indicating a more favourable effect of a softer membrane. For a Mack mode with a specified dimensional frequency – since its dimensionless frequency, normalised by the local boundary-layer thickness and oncoming velocity, increases as it propagates downstream – the second-mode frequency band usually appears in downstream locations, and so does the stabilising effect of the membrane. Thus it is favourable to apply a compliant panel at a downstream region. In this situation, the solid–compliant junction could produce an additional scattering effect on the evolution of the Mack mode due to the sudden change of its boundary condition. The scattering effect is quantified by a transmission coefficient defined by the equivalent amplitude of the compliant-wall perturbation to the solid-wall perturbation, which can be obtained by the harmonic linearised Navier–Stokes (HLNS) approach. If the admittance is weak, then the transmission coefficient can also be predicted by an analytical solution based on the residue theorem. It is found that most of the second modes are suppressed by the scattering effect as long as the argument of the admittance is in the interval $[150^\circ, 210^\circ ]$ , agreeing with most of the physical situation. The analytical predictions agree well with the HLNS calculations when the modulus of the admittance is less than $O(0.1)$ .

Effects of hump deflection angle on streamwise vortex instability over a yawed cone at Mach 6

This paper investigates the influence of three-dimensional smooth humps with varying deflection angles (φ) on the linear stability of streamwise vortices over a yawed cone with a 7° half-angle at a 6° angle-of-attack, free-stream Mach number of 6, and unit Reynolds number of 1.0×107/m. The steady laminar flow is obtained using direct numerical simulations. The eN method based on global stability theory is used to predict the transition location of the streamwise vortices along the centerline on the leeward side of the cone. The results reveal that φ plays a significant role in the outward vortex generation location, with smaller values of φ effectively delaying the outward vortex generation. Moreover, there is a qualitative relationship between the instability of the streamwise vortices and the inward/outward vortex structure characteristics of the base flow over a yawed cone. Namely, the transition delay effect of the streamwise vortices is proportional to the delay in the generation location of the outward vortex, which provides insights into the control of the transition induced by streamwise vortices. In particular, the configuration based on a hump with φ=9° and a height of 0.57 times the local boundary layer thickness delays the transition by approximately 38.2% at the critical N-factor (Ntr=12.5) without significantly increasing the instability of the inner mode.

Influence of skewed three-dimensional sinusoidal surface roughness on turbulent boundary layers

The impact of roughness skewness (ksk) on turbulent boundary layer (TBL) flow with a zero pressure gradient over three-dimensional (3D) sinusoidal rough surfaces was experimentally investigated using a single hotwire anemometer. Nine 3D sinusoidal profiles were manufactured with positive, negative, and zero roughness skewness values. Measurements were taken at three different freestream velocities for each surface and compared with smooth wall TBL results. This study covered a range of friction Reynolds numbers (Reτ) from approximately 1000 to 4000, with δ/k≈20 ± 2, where δ represents the local boundary layer thickness, and k is the maximum height of the roughness, measured from the valley to peak. The results indicate that the wall-unit normalized streamwise mean velocity profiles for all rough surfaces exhibit a downward shift compared to the smooth wall profiles. Surfaces with positive roughness skewness produced the highest drag, leading to the largest downward shift. The friction coefficient (Cf) decreased as ksk decreased. The percentage increase in Cf and ΔU+ (the roughness function) was much larger when moving from negative to zero roughness skewness than when moving from zero to positive roughness skewness. The small differences in turbulence intensity profiles and higher-order turbulence statistics in the outer region of the TBL support the outer layer similarity hypothesis for the roughness considered in this study. The autocorrelation study revealed that surfaces with positive roughness skewness tend to shorten the average length of turbulence structures in the near-wall region.

Spatial and temporal alterations due to vortex generators in a flare induced shock–boundary layer interaction

This paper describes the modifications instigated in a flare induced shock–boundary layer interaction flowfield by two vortex generators viz. Baseline Ramps (BRs) and Ramped Vanes (RVs). Experimental and computational investigations were conducted at Mach 2, on a cone–cylinder–flare model, with a flow turning angle of 24° at the cylinder–flare juncture. The vortex generators were placed 50 mm (10δ) upstream of the compression corner and their height was 50% of the local boundary layer thickness (h = 2.1 mm = 0.5δV G). The counter-rotating vortices emanated by Baseline Ramps (BRs), remained in close proximity to one another and interacted strongly along the upwash regions. Hence, they quickly dissipated and moved away from the model surface, causing only a nominal impact on the interaction region. Alternatively, the vortices produced by Ramped Vanes (RVs) were amply separated and therefore, largely retained their core strength and were not rapidly advected away from the near-wall region. As a result, the separation occurred a little prematurely in the upwash regions and was significantly delayed along the downwash regions. Additionally, tornado-like vortices were formed, due to the streamwise vortices interacting with the separation bubble. The delay in separation along the downwash regions, also brought the separation shock closer to the compression corner. This was accompanied by a suitable increase in the shock’s oscillating frequency, in such a way that the Strouhal number based on the interaction length (distance between the corner and the mean position of the separation shock foot) remained more or less the same.

Investigating roughness effects on ship resistance in shallow waters

Shallow waters influence the behaviour and performance of a vessel by modifying the local pressure distribution, wave making, and boundary layer thickness. The boundary layer thickness is also influenced by surface roughness. No previous studies have investigated the combined effects of shallow water contributions and roughness on ship resistance. This study aims to fill this knowledge gap in the literature by using Unsteady Reynolds Averaged Navier-Stokes modelling. Results show that the total resistance coefficient increases between approximately 22% and 36% in the presence of roughness depending on the speed and depth-to-draft ratio. The numerical model used shows that pressure resistance grows at a faster pace than frictional resistance and increases its relative contribution to the total when roughness is applied, contrary to deep water cases.

Control of bow shock induced three-dimensional separation using bleed through holes

The unsteady three-dimensional separated flow on a wall induced by a square protrusion (approximately twice the local boundary layer thickness in width and height), and its control by means of passive suction through holes, is investigated using wind tunnel experiments at Mach 2.87. The baseline flow without any control was characterized and compared against the cases with bleed. A bow-shaped separation line on the wall with a mid-span separation length of 5.57δ from protrusion face was traced from the oil-flow visualization. The averaged pressure distribution surveyed using static pressure ports placed on the wall has mapped plateau, high-pressure, and low-pressure regions in the separated flow, distinctive to three-dimensional interactions. Ten control configurations were tested with suction holes placed along mid-span in the different pressure regions. Significant spanwise “Mean Reduction in Separation Length” of up to 0.93δ was observed from oil-flow visualization. A comparison of observations from various control configurations suggested that bleeding the flow from the high-pressure region could delay the separation and reduce the bubble size in general. Furthermore, time-resolved Schlieren visualizations have confirmed reduction in both “mid-span separation length” and “shock-intermittent-region” with the introduction of suction in high-pressure region. Fourier and Proper Orthogonal Decomposition analysis done on the Schlieren data has confirmed the presence of low-frequency separation-shock oscillations at Strouhal Numbers of order 10−2, both with and without control. Furthermore, the amplitudes of separation-shock oscillations in the spectrum were reduced with the introduction of suction simultaneously from two holes placed in high- and low-pressure regions.

Effect of Reynolds number on second-mode waves in transitional hypersonic boundary layers

The second-mode instability plays an important role in the natural transition of hypersonic boundary layer. In this paper, the Reynolds number effect on the second-mode waves has been experimentally investigated using the Nanoparticle-tracer based Planar Laser Scattering (NPLS) technique and PCB® fast response pressure sensors in Mach 6 quiet wind tunnel. The flow visualization results clearly capture the rope-like second-mode waves and the “quiet zone” before breakdown. The wavelength of second-mode waves is approximately twice the local boundary layer thickness, increasing with the streamwise distance and decreasing with the Reynolds number. The time delays between sensors indicate no significant Reynolds number effect on the propagation velocity of second-mode waves. The average velocity is about 0.82Ue. The characteristic frequencies are collated at different streamwise locations under different Reynolds numbers and show a linear proportion to Re/x. Based on the growth law of compressible conical boundary layer thickness, the characteristic frequency relation and wavelength relation are derived as a function of Reynolds number and streamwise distance. The theoretical estimation values agree well with the experimental results, which provides the potential feasibility to predict the characteristic frequency and wavelength in other tunnels.

Heat transfer and behavior of the Reynolds stress in Mach 6 boundary layer transition induced by first-mode oblique waves

This paper investigates a Mach 6 oblique breakdown via direct numerical simulation in conjunction with stability and quadrant analyses. Particular emphasis is placed on, first, the heat transfer and mean flow distortion in the near-wall and outer transitional boundary layer, and, second, the flow events that are responsible for the production of the Reynolds stress. The energy budget reveals that enhancement of viscous dissipation due to mean flow distortion dominates the heat transfer overshoot, while the dissipation due to fluctuations is lesser but not negligible. Downstream of the location of the peak mean heat flux, the wall temperature gradient (non-dimensionalized by the freestream temperature and local boundary layer thickness) varies little, owing to the occurrence of breakdown and the establishment of self-similarity. Renormalized by the boundary layer thickness, a new correlation of the Stanton number shows no overshoot or difference between the original overshoot region and the turbulent region, which indicates the possibility of similarity once breakdown has occurred. In the outer region, enhanced advective heat exchange strongly reshapes the mean temperature profile. Because of successive modal growth and nonlinear saturation, the contributions of the primary oblique mode, streak mode, and a superharmonic to the outer advective heat transfer are found to compete near the location of the peak heat flux. From the perspective of fluid motions, quadrant analysis highlights the evenly and broadly distributed joint probability density function (PDF) of the fluctuating velocities during transition, which results in overproduction of the Reynolds stress, while the PDF is concentrated around zero in the turbulent region. The flow event Q2 (ejection) overtakes Q4 (sweep) in the outer boundary layer of the transitional region, mainly owing to the primary mode, while the two events become attenuated and nearly achieve balance when transition is complete.

Interaction between a stationary sphere and turbulent flow in a boundary layer

We investigate the interaction of a stationary sphere with turbulent flows in a spatially developing boundary layer over a flat plate by means of fully resolved direct numerical simulations. The diameter of the sphere D is much larger than the Kolmogorov length scale. The sphere Reynolds number ReD is changed by varying the sphere diameter, while the gap ratio is held constant with G/D=0.1, where G is the distance between the bottom of the sphere and the flat plate. The simulation results indicate that there exist complex interactions between the small-scale vortex in the wake of the sphere and the large-scale coherent structures inside the turbulent boundary layer. The jet-like flow through the gap is deflected away from the wall, and the level of deflection increases with ReD. As a result, asymmetrical flow structures are observed in the recirculation zone. In addition, the mean recirculation length is found to decrease with the increase in ReD. Concerning the turbulence modulation, statistics show that the skin-friction drag and boundary layer thickness are decreased in the recirculation region with respect to the undisturbed flow, whereas the displacement thickness is increased due to the presence of reverse flow. These effects become more pronounced as ReD increases. The budget of the turbulent kinetic energy in the sphere wake is also examined. It is revealed that the turbulent production and viscous dissipation rate are significantly enhanced under the effect of the sphere with size of the same order of magnitude as the local boundary layer thickness.

Effect of exit geometry of blowing air on friction drag of an underwater plate

Air layer drag reduction (ALDR) is one of the important techniques for reducing the frictional resistance of ships and underwater vehicles. The air injection configuration directly influences air layer coverage on the surface and hence drag reduction. Several shapes of air exit have been investigated in the past, including narrow slots, regular-shaped holes, porous media, and arrays/combinations of them. A new exit shape, i.e. modified Nekomimi, is proposed and investigated numerically for ALDR of an underwater flat plate. The work is inspired by air film cooling technology where it is desirable to have an air layer segregating wall from main gas flow. The Reynolds number examined is 6970–22890, based on local turbulent boundary layer thickness, for the incoming water flow or 700–5550, based on the equivalent exit diameter of blowing air. Results show that the Nekomimi exit produces a larger and more even air layer coverage, as indicated by the air volume fraction on the plate, accounting for a more pronounced drag reduction and net energy saving than a circular exit with the same area or spanwise dimension. Multi-Nekomimi-exit arrangement is also investigated to obtain a larger air-layer coverage on the plate, showing good promise in engineering applications.

The Wake Structure of a Stationary and a Rotary Wall-Mounted Low-Aspect-Ratio Cylinder

This paper investigates the wake structure of a low-aspect-ratio rotating cylinder mounted wall-normal to a flat plate at a diameter-based Reynolds number of . The cylinder is driven at a constant rotational rate about its respective axial coordinate. Four nondimensional rotation rates were selected: 0.5, 1, 2, and 3, representing rates based on the static cylinder’s natural shedding frequency and corresponding harmonics. Two aspect ratios were investigated: i) and ii) . The case of represents a cylinder height equal to the local boundary-layer thickness. Both streamwise and cross-stream (transverse) particle image velocimetry (PIV) planes are presented, and the resulting time-averaged flowfield is examined. Results for the rotating cylinder reveal the development of a dominant streamwise vortex that persists for several length scales downstream of the cylinder. Accompanying the streamwise vortex formation is an enhancement in the wall-normal velocity component (downwash) behind the rotating cylinder. Additionally, the maximum downwash occurs immediately behind the rotating cylinder near 0.27 diameters downstream in contradistinction to a stationary cylinder with peak downwash near 2–3 diameters. The maximum downwash, being in line with the formation of the dominant streamwise vortex, shortens the recirculation region in the cylinder’s wake, thus shifting the plate reattachment point further upstream. In the case of , where the cylinder is submerged within the boundary layer, although the length of the recirculation region reflected by the mean flow is lengthened by the rotary motion, the maximum downwash for the rotating cylinder is enhanced by a factor of 10 from that of the maximum downwash experienced by a static counterpart.

Effect of three-dimensional smooth humps on hypersonic boundary layer instability of streamwise vortices over a yawed cone

This paper describes the design of a class of three-dimensional (3D) smooth humps mounted on a yawed cone model for a high-precision compressible Navier–Stokes solver. The influence of isolated 3D humps with different heights on the linear stability of streamwise vortices over a yawed cone with a 7° half-angle at a 6° angle-of-attack, free-stream Mach number of 6, and unit Reynolds number of 1.0×107/m is investigated. The results show that smooth humps induce stationary streaks inside the streamwise vortices over a yawed cone, effectively increasing the energy of the inward vortex and inhibiting the evolution and development of the outward vortex. Stability analysis shows that the induced streaks enhance the inner mode instability, suppress the outer mode instability, and reduce the dominant frequency of the outer mode. The stability properties of the hump-induced streaks are studied, and the physical process of the transformation between the new streak instability mode and the original boundary layer mode is revealed. The eN method based on global stability theory is used to predict the transition location along the centerline on the leeward side of the cone. It is found that configurations with hump heights of 0.153 and 0.267 times the local boundary layer thickness result in a transition delay of ∼3% and ∼11%, respectively.

Investigation of shock dynamics in an axisymmetric inlet/isolator with attached boundary layers

Abstract

Wall pressure beneath a transitional hypersonic boundary layer over an inclined straight circular cone

Properties of wall pressure beneath a transitional hypersonic boundary layer over a 7∘ half-angle blunt cone at angle of attack 6∘ are studied by Direct Numerical Simulation. The wall pressure has two distinct frequency peaks. The low-frequency peak with f≈10−50 kHz is very likely the unsteady crossflow mode based on its convection direction, i.e. along the axial direction and towards the windward symmetry ray. High-frequency peaks are roughly proportional to the local boundary layer thickness. Along the trajectories of stationary crossflow vortices, the location of intense high-frequency wall pressure moves from the bottom of trough where the boundary layer is thin to the bottom of shoulder where the boundary layer is thick. By comparing the pressure field with that inside a high-speed transitional swept-wing boundary layer dominated by the z-type secondary crossflow mode, we found that the high-frequency signal originates from the Mack mode and evolves into the secondary crossflow instability.

Development and validation of a mathematical model to predict the thermal behaviour of nanofluids

With a single-phase approach, a 3D mathematical model was developed through Computational Fluid Dynamics (CFD) techniques, coupling the momentum and heat transfer balances for the study of the thermal behaviour of nanofluids. The local heat transfer coefficient and thermal boundary layer thickness of CuO/water, Fe2O3/water and Al2O3/water nanofluids, have been predicted and compared with those experimentally determined at three volume concentration of nanoparticles (ϕ=0.01%, 0.03% and 0.05%), at T = 25 °C and T = 55 °C for laminar and turbulent flow conditions, using a newly developed sophisticated noninvasive heat transfer coefficient probe that is flush mounted on the inner wall of the test section. Such conditions have been used for the mathematical model, considering the effects of the nanoparticle materials and volume concentrations through effective thermophysical properties. The predicted results from the mathematical model show a good agreement with the trend and the experimental observations. The enhancement of the heat transfer coefficient and reduction of the thermal boundary layer when increasing the volume concentration of the nanofluids and when increasing the flow rates have been properly predicted by the mathematical model results, showing average absolute relative errors between 1.7% and 8.4%. The model exhibits an enhancement in the agreement between the experimental measurements and the predicted results when comparing with other models found in literature.

Optimal perturbations and transition energy thresholds in boundary layer shear flows

Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this work, we employ adjoint-based optimization to identify optimal initial perturbations in the Blasius boundary layer, culminating in the computation of the subcritical transition critical energy threshold and the associated fully localized critical optimum in a spatially extended configuration, the so called minimal seed. By dynamically rescaling the variables with the local boundary layer thickness, we show that the identified edge trajectory approaches the same attracting phase space region as previously reported edge trajectories, and reaches the region more efficiently.