Turbulent Boundary Layer Research Articles

Dynamics and structure of network magnetic fields: Supergranular vortex expansion-contraction

Abstract We report on the formation of a large magnetic coherent structure in a vortex expansion-contraction interval, resulting from the merger of two plasmoids driven by a supergranular vortex observed by Hinode in the quiet-Sun. Strong vortical flows at the interior of vortex boundary are detected by the localized regions of high values of the Instantaneous Vorticity Deviation, and intense current sheets in the merging plasmoids are detected by the localized regions of high values of the Local Current Deviation. The spatiotemporal evolution of the line-of-sight magnetic field, the horizontal electric current density, and the horizontal electromagnetic energy flux is investigated by elucidating the relation between velocity and magnetic fields in the photospheric plasma turbulence. A local and continuous amplification of magnetic field from 286 G to 591 G is detected at the centre of one merging plasmoid during the vortex expansion-contraction interval of 60 min. During the period of vortex contraction of 22.5 min, the line-of-sight magnetic field at the centre of plasmoid-1 (2) exhibits a steady decrease (increase), respectively, indicating a steady transfer of magnetic flux from plasmoid-1 to plasmoid-2. At the end of the vortex expansion-contraction interval, the two merging plasmoids reach an equipartition of electromagnetic energy flux leading to the formation of an elongated magnetic coherent structure encircled by a shell of intense current sheets. Evidence of the disruption of a thin current sheet at the turbulent interface boundary layers of two merging plasmoids is presented.

High-fidelity simulations of microramp-controlled shock wave/boundary layer interaction

Microvortex generators (MVGs) are a promising solution to control shock wave/turbulent boundary layer interactions (SBLIs), especially in supersonic inlets. In this study, we examine the effects of a microramp vortex generator on an SBLI generated by an oblique shock wave and a turbulent boundary layer using direct numerical simulations (DNSs). Two cases, with and without the presence of a microramp, are compared in terms of their mean and unsteady flow features at free-stream Mach number equal to 2 and friction Reynolds number at the inviscid shock impingement equal to 600. The long integration period allows us to assess how microramps affect the typical low-frequency unsteadiness observed in SBLIs, and the data generated may serve as a reference for simulations of lower fidelity or reduced order models. The analysis shows that the three-dimensional microramp wake alters the interaction region dramatically, inducing a significant spanwise modulation and topology change of the separation. For example, tornado-like structures redistribute the flow in both the spanwise and wall-normal directions inside the recirculation region. The increase in momentum close to the wall by the ramp vortices effectively delays the onset of the separation and, thus, the separation length, but at the same time leads to a significant increase in the intensity of the wall-pressure fluctuations. We then characterise the mutual interaction between the arch-like vortices around the ramp wake and the SBLI. The specific spanwise vorticity shows that these vortices follow the edge of the separation and their intensity, apart from mean compressibility effects, is not affected by the shocks. The shocks, instead, are deformed in shape by the periodic impingement of the vortices, although the spectral analysis did not reveal any significant trace of their shedding frequency in the separation region. These Kelvin–Helmholtz vortices, however, may be relevant in the closure of the separation bubble. Fourier analysis also shows a constant increase, in both value and magnitude, in the low-frequency peak all along the span, suggesting that the motion of the separation shock remains coherent while being disturbed by the arch-like vortices and oscillating at a higher frequency in absolute terms.

The analysis of Gurney flap applications for autonomous underwater gliders

ABSTRACT In this paper, the Gurney flap structure (GF) from aeronautical research was applied to underwater gliders for improving the lift-to-drag ratio. Firstly, the numerical simulation method was used to verify the lift enhancement principle of the GF structure and the feasibility of its application to autonomous underwater gliders (AUG). Secondly, the performance of different GF was simulated and analysed, and a variable GF structure was proposed with the requirements of the operating modes. The GF parameters were optimised by a genetic algorithm. The results show that the performance of GF in water is similar to that in air, so it is feasible to apply GF to AUG. When the height of GF is close to the turbulent boundary layer of the trailing edge of the wing, the lift-to-drag ratio is significantly improved, especially in the range of small angle of attack and the maximum increase is up to 30%.

Direct numerical simulation of a supersonic turbulent boundary layer with hydrogen combustion

Direct numerical simulation of a supersonic turbulent boundary layer with hydrogen combustion

The impact of finite span and wing-tip vortices on a turbulent NACA0012 wing

High-fidelity simulations are conducted to investigate the turbulent boundary layers around a finite-span NACA0012 wing with a rounded wing-tip geometry at a chord-based Reynolds number of $Re_c=200\,000$ and at various angles of attack up to $10^\circ$ . The study aims to discern the differences between the boundary layers on the finite-span wing and those on infinite-span wings at equivalent angles of attack. The finite-span boundary layers exhibit: (i) an altered streamwise and a non-zero spanwise pressure gradient as a result of the variable downwash induced by the wing-tip vortices (an inviscid effect typical of finite-span wings); (ii) differences in the flow history at different wall-normal distances, caused by the variable flow angle in the wall-normal direction (due to constant pressure gradients and variable momentum normal to the wall); (iii) laminar flow entrainment into the turbulent boundary layers near the wing tip (due to a laminar–turbulent interface); and (iv) variations in boundary layer thickness across the span, attributed to the variable wall-normal velocity in that direction (a primarily inviscid effect). These physical effects are then used to explain the differences in the Reynolds stress profiles and other boundary layer quantities, including the reduced near-wall peak of the streamwise Reynolds stress and the elevated Reynolds stress levels near the boundary layer edge, both observed in the finite-span wings. Other aspects of the flow, such as the downstream development of wing-tip vortices and their interactions with the surrounding flow, are reserved for future investigations.

Limiting regimes of turbulent horizontal convection. Part 1. Intermediate and low Prandtl numbers

We report the existence of two new limiting turbulent regimes in horizontal convection (HC) using direct numerical simulations at intermediate to low Prandtl numbers. In our simulations, the flow is driven by a step-wise buoyancy profile imposed at the surface, with free-slip, no-flux conditions along all other boundaries, except along the spanwise direction, where periodicity is assumed. The flow is shown to transition to turbulence in the plume and the core, modifying the rate of heat and momentum transport. These transitions set a sequence of scaling laws that combine theoretical arguments from Shishkina, Grossmann and Lohse (SGL) and Hughes, Griffiths, Mullarney and Peterson (HGMP). The parameter range extends through Rayleigh numbers in the range [ $6.4\times 10^5, 1.92\times 10^{15}$ ] and Prandtl numbers in the range [ $2\times 10^{-3},2$ ]. At low Prandtl numbers and intermediate Rayleigh numbers, a core-driven regime is shown to follow a Nusselt-number scaling with $Ra^{1/6}Pr^{7/24}$ . For Rayleigh numbers larger than $10^{14}$ , the Nusselt number scales with $Ra^{0.225}Pr^{0.417}$ . For these particular regimes, the Reynolds number is found to scale as $Ra^{2/5}Pr^{-3/5}$ for the low-Prandtl-number regime and $Ra^{1/3}Pr^{1}$ for Rayleigh numbers larger than $10^{14}$ . These results embed the HGMP model in the SGL theory and extend the known regime diagram of HC at high Rayleigh numbers. In particular, we show that HC and Rayleigh–Bénard share similar turbulent characteristics at low Prandtl numbers, where HC is shown to be ruled by its core dynamics and turbulent boundary layers. This new scenario confirms that fully turbulent HC enhances the transport of heat and momentum with respect to previously reported regimes at high Rayleigh numbers. This work provides new insights into the applicability of HC for geophysical flows such as overturning circulations found in the atmosphere, the oceans, and flows near the Earth's inner core.

Experimental observations on Weissenberg number-controlled developing turbulent boundary layers

Experimental observations on Weissenberg number-controlled developing turbulent boundary layers

Steady secondary flow in a turbulent boundary layer past a slender axisymmetric body

The turbulent boundary layer in a viscous incompressible fluid developing longitudinally past the surface of a thin cone or cylinder at a finite distance from the laminar–turbulent transition zone is studied. The characteristic Reynolds number, determined from the external flow velocity and the length of the body, is assumed to be large, and the thickness of the boundary layer is small and comparable to the radius of the body. The asymptotic method of multiple scales is used to find solutions to the Navier–Stokes equations. Instead of the traditional decomposition of the solution into time-averaged values and their fluctuations, the velocities and pressure are expressed as an asymptotic series consisting of steady and perturbed terms. As a result, the viscous steady flow (‘secondary’) that arises in the boundary layer as a mandatory component of fast turbulent fluctuations was described. Analytical and numerical solutions for the radial steady velocity are presented, describing the self-induced suction of fluid from the external flow into the boundary layer. Further analytical solutions are obtained for the longitudinal and circumferential velocities, which differ markedly from the laminar regime. The solutions found are somewhat similar to the degenerate (one-dimensional) case of self-sustaining longitudinal thin structures in turbulent shear flows. A qualitative comparison with direct numerical simulations is presented.

Impact of Blowing and Density Ratio on the Film Cooling and Heat Transfer in an Aggressive Turbine Center Frame

Abstract It was shown in the previous study that the aft purge flows from the last stage of the high-pressure turbine (HPT) have a significant film cooling potential in the downstream turbine center frame (TCF) (Jagerhofer et al., 2023, “Heat Transfer and Film Cooling in an Aggressive Turbine Center Frame,” ASME J. Turbomach., 145(12), p. 121012). The TCF is a stationary duct that guides the flow from the HPT outlet to the low-pressure turbine (LPT) inlet and is the third most thermally loaded engine component. This article investigates the impact of different purge-to-mainstream blowing and density ratios on the film cooling effectiveness and the heat transfer coefficient in the TCF. The experiments were conducted in a product-representative 1.5-stage HPT-TCF-LPT vane configuration under Mach-similarity in the Transonic Test Turbine Facility (TTTF) at TU Graz. The blowing ratio has been demonstrated to be the dominant parameter for purge film cooling in TCFs since HPT purge flows typically have very low momentum. Even at twice the nominal blowing ratio, no cooling film detachment was observed on the TCF hub or shroud surface. Varying the density ratio in the experimentally possible range delivered no significant differences in the results. With increasing purge blowing ratios, the film cooling effectiveness in the TCF increases as expected, but the heat transfer also intensifies due to the purge injection. The circumferentially averaged film cooling on the hub scales relatively well with an offset version of the well-known Hartnett correlation (Hartnett et al., 1961, “Velocity Distributions, Temperature Distributions, Effectiveness and Heat Transfer for Air Injected Through a Tangential Slot Into a Turbulent Boundary Layer,” ASME J. Heat Transfer, 83(3), pp. 293–305) that takes into account the ingress-induced premixing of the purge flow in the cavities.

Mechanisms and models of the turbulent boundary layers at transcritical conditions

Mechanisms and models of the turbulent boundary layers at transcritical conditions

Numerical simulation of shock attenuation with real gas effects and a turbulent boundary layer in the expansion tube

AbstractThe influence of real gas effects and a turbulent boundary layer on shock wave attenuation in the expansion tube is studied by numerically solving the axisymmetric compressible Navier–Stokes equations with an adaptive mesh refinement technique. Numerical simulation results reveal that the ideal gas assumption is not applicable to the expansion tube, and the turbulent boundary layer plays a major role in decreasing the shock wave speed in the acceleration tube of the expansion tube. Shock wave attenuation is attributed to the turbulent boundary layer decreasing the pressure behind the shock wave. The numerical simulations that include the real gas effects and the development of turbulent boundary layers qualitatively agree with analytical solutions in the shock tube, and they show good agreement with the experimental results, especially for the shock speed in the acceleration tube of the expansion tube. Both effects should be considered in the numerical simulation model aimed to support experiments in expansion tubes.

An integral method for estimating wall heat flux in spatially developing turbulent boundary layers

An integral method for estimating wall heat flux in spatially developing turbulent boundary layers

Momentum and kinetic energy transport in supersonic particle-laden turbulent boundary layers

Momentum and kinetic energy transport in supersonic particle-laden turbulent boundary layers

Streamwise energy-transfer mechanisms in zero- and adverse-pressure-gradient turbulent boundary layers

The present study investigates streamwise ( $\overline {u^2}$ ) energy-transfer mechanisms in the inner and outer regions of turbulent boundary layers (TBLs). Particular focus is placed on the $\overline {u^2}$ production, its inter-component and wall-normal transport as well as dissipation, all of which become statistically significant in the outer region with increasing friction Reynolds number ( $Re_{\tau }$ ). These properties are analysed using published data sets of zero, weak and moderately strong adverse-pressure-gradient (APG) TBLs across a decade of $Re_{\tau }$ , revealing similarity in energy-transfer pathways for all these TBLs. It is found that both the inner and outer peaks of $\overline {u^2}$ are always associated with local maxima in the $\overline {u^2}$ production and its inter-component transport, and the regions below/above each of these peaks are always dominated by wall-ward/away-from-wall transport of $\overline {u^2}$ , thereby classifying the $\overline {u^2}$ profiles into four distinct regimes. This classification reveals existence of phenomenologically similar energy-transfer mechanisms in the ‘inner’ and ‘outer’ regions of moderately strong APG TBLs, which meet at an intermediate location coinciding with the minimum in $\overline {u^2}$ profiles. Conditional averaging suggests existence of similar phenomena even in low $Re_{\tau }$ canonical and/or weak APG TBLs, albeit with the outer-region mechanisms weaker than those in the inner region. This explains the absence of their $\overline {u^2}$ outer peak and the dominance of $\overline {u^2}$ wall-normal transport away from the wall, which potentially originates from the inner region. Given that the wall-ward/away-from-wall transport of $\overline {u^2}$ is governed by the $Q_4$ (sweeps)/ $Q_2$ (ejections) quadrants of the Reynolds shear stress, it is argued that the emergence of the $\overline {u^2}$ outer peak corresponds with the statistical dominance of $Q_4$ events in the outer region. Besides unravelling the dynamical significance of $Q_2$ and $Q_4$ events in the outer region of TBLs, the present analysis also proposes new phenomenological arguments for testing on canonical wall-turbulence data at very high $Re_{\tau }$ .

Small-scale Helmholtz resonators with grazing turbulent boundary layer flow

ABSTRACT Helmholtz resonators flush-mounted in a wall beneath turbulent boundary layer flow are studied by focusing on their flow-induced excitation and effect on the grazing turbulent flow. A particular focus lies on single resonators tuned to the most intense spatio-temporal fluctuations in the near-wall vertical velocity and wall-pressure, residing at a spatial scale of λ x + ≈ 250 (or temporal scale of T + ≈ 25 ). Resonators are examined in a boundary layer flow at R e τ ≈ 2280 . Two neck-orifice diameters of d + ≈ 68 and 102 are considered, and for each value of d + three different resonance frequencies are studied (corresponding to a period of T + ≈ 25 , as well as one lower, and one higher, period). The response of the TBL flow is analysed by employing velocity data from hot-wire anemometry and particle image velocimetry measurements. Passive resonance only affects streamwise velocity fluctuations in the region y + ≲ 25 , while vertical velocity fluctuations due to resonance reach up to y + ≈ 100 . A narrow-band increase in streamwise turbulence kinetic energy at the resonance scale co-exists with a more than 20% attenuation of lower-frequency energy. Current findings on single resonator cases will aid in the development of passive surfaces with distributed resonators for boundary-layer flow control.

A vibration-based method to estimate the low-wavenumber wall pressure field in a turbulent boundary layer

When an elastic structure is excited by a low-speed turbulent flow, it generates flow-induced vibration which is primarily due to the low-wavenumber components of the wall pressure field (WPF) beneath the turbulent boundary layer (TBL). Therefore, to accurately predict the vibration response of the structure, an accurate estimation of the low-wavenumber WPF is needed. While existing TBL models for WPF well predict the convective region, they exhibit significant discrepancies in predicting the low-wavenumber levels. This numerical study aims to explore the feasibility of estimation of the low-wavenumber WPF by analysing vibration data obtained from a structure excited by a TBL. An inverse method is proposed based on the relationship between the TBL forcing function and structural vibrations in the wavenumber domain. The random TBL force is simulated with deterministic loading using the uncorrelated wall plane wave technique. A model of a simply supported plate under a TBL excitation is developed to demonstrate the proposed method. The plate's acceleration data is then used to estimate the WPF in the low-wavenumber range. It is shown how using multiple discrete frequencies in the analysis can reduce the required snapshots for accurate estimation of the WPF.

Experimental validation of vibration similitude laws for stiffened panels excited by a turbulent boundary layer

Stiffened structures excited by a turbulent boundary layer (TBL) occur in many engineering applications, particularly in the aerospace and naval sectors. The structures encountered in these applications are generally large and complex, and carrying out experiments in order to characterize their vibration response can be costly, time-consuming and difficult. To overcome these constraints, the similitude theory can be used to estimate the response of a full scale structure from the response of a reduced scale structure. A simplifying step to determine these similitude laws for stiffened panels consists in modeling the panel as an equivalent orthotropic panel. Then, using the governing equation of the orthotropic panel and considering the TBL excitation, the vibration similitude laws are derived implying similitude conditions to be respected on geometrical and material properties of the structure as well as flow velocity. In this paper, we present the developments of these similitude laws and an experimental validation for panels in air. The similitude conditions are discussed to adequately choose the properties of scaled stiffened panels. Experimental results are presented to show that the structural response of the reference panel can be recovered from the response of the reduced scale panel using the related scaling laws.

Computation of Green's functions for the acoustic scattering by an elastic structure excited by a turbulent flow in water

To model the hydrodynamic noise produced by an elastic ship hull or propeller excited by a turbulent boundary layer, we need an efficient method to compute the acoustic scattering by an elastic body surrounded by a fluid. In 3D, Boundary Element Methods (BEM) are used to reduce the computational costs, for both the fluid and the elastic body. A natural way to compute the boundary integral representation (BIR) of the sound pressure is to use formulations based on the free space acoustic and elastic Green's functions. However, since the turbulent flow along the elastic body is known only statistically, the use of these Green's functions would be too expensive. A remedy is to compute a Green's function adapted to the physical problem, thus satisfying the transmission conditions of the fluid-structure problem. This so-called "tailored Green's function" is determined by solving a coupled acoustic-elastic problem with the BEM, and leads to a simplified BIR of the sound pressure compatible with a stochastic source term. We first validate the computation of the tailored Green's function over a classic spherical geometry. Then we compare the scattering of multiple quadrupoles by elastic or rigid NACA0012 profiles.

Coupling deflectometry measurements on membranes to the force analysis technique: opportunities and challenges

This work is grounded on the force analysis technique, an identification method that directly uses a structure's equation of motion to formulate an inverse problem, explicitly identifying the force causing the system's motion. This technique has mainly been applied on heavy objects since contact vibration measurements using accelerometers on light and thin structures are biased by the added mass and are complex to setup. Using non-contact and full-field vibration measurements (here, deflectometry), opens the possibility of applying the force analysis technique to such structures. This research aims to investigate the opportunities offered by the identification of space-time varying loadings of various types (acoustical, mechanical, and turbulent boundary layer) all these loadings being applied on a membrane. Through this study, we also strive to highlight the challenges and opportunities brought by of coupling non-contact and full-field measurements on membranes to the force analysis technique.

Study and modeling of the ultrasonic ambient noise induced by the fluid-structure interaction in a pipe

An elastic guided wave-based structural health monitoring (SHM) system consists in examining the integrity of a structure through the propagation of elastic waves. In this context, passive methods turn initial hindrances into advantages by making use of the ambient ultrasonic noise in a structure in operation, through the cross-correlation. Although they have been empirically applied in several configurations, no model is available to predict the link between the flow regime and the convergence of the ambient noise correlation towards the impulse response of the system. Considering the different parameters involved in the case of a pipe, a physical approach of this issue may be studied through the turbulent boundary layer, which has long been described by the Corcos model. Corcos-like models have essentially been applied so far on the audible range, below 1 kHz, where we are interested in frequencies around 100 kHz, typical for SHM applications. The semi-empirical model allows to determine a wall boundary pressure, which, applied at the pipe's inner boundaries, acts as a source term for ultrasonic elastic waves propagating in the pipe. Our goal is then to study if such a model can be used at these high frequencies to reproduce the experimental observations.