Boundary Layer Subject Research Articles

A streamline coordinate analysis of a turbulent boundary layer subject to pressure gradients and curvature on the windward side of a bump

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favourable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterised and compared with a lower-Reynolds-number flow over the same geometry. The momentum budgets are analysed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral-analysis-based approximations for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. The shear and wall-normal Reynolds stress profiles normalised by these approximations exhibit a better collapse compared with friction velocity and Zagarola–Smits normalisations in the strong favourable pressure gradient region and in the mild adverse pressure region that precedes it in this flow. Simplification of these Reynolds stress approximations along with results from the DNS are used to obtain semi-empirical approximations that are able to provide stress closure in terms of wall solution fields for the turbulent boundary layer under consideration.

Hiemenz stagnation point flow of a second-order micropolar slip flow with heat transfer

Purpose This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions. Design/methodology/approach The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions. Findings The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases. Originality/value The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

Heat transfer modification in an unsteady laminar boundary layer subject to free-stream traveling waves

A laminar, thermal boundary layer was forced computationally by free-stream, traveling-wave velocity fluctuations and the effects on the wall heat flux and skin friction were measured as a function of the phase speed of the disturbances and the streamwise location along the developing flow. The heat flux modification due to the flow forcing was significantly higher than the corresponding skin friction enhancement, and the dependence of these two transport properties on the phase speed was qualitatively different. The skin friction modification exhibited a maximum at an optimal phase speed, which was explained in terms of the overlap of two distinct viscous layers within the boundary layer. The heat flux modification did not exhibit this maximum, although evidence was found to suggest such a maximum may occur with sufficient boundary layer development. Because the magnitude of the wall heat-flux modification scales quadratically with wave amplitude, traveling wave disturbances pose significant challenges for thermal transport measurements in periodically perturbed environments, like turbomachinery, but also new opportunities for the control of heat transfer.

Improved convergence of the spectral proper orthogonal decomposition through time shifting

Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to response modes from resolvent analysis. The SPOD, coupled with the Welch method for spectral estimation, may require long time-resolved datasets. In this work, a linearised Ginzburg–Landau model is considered in order to study the method's convergence. Spectral proper orthogonal decomposition modes of the white-noise forced equation are computed and compared with corresponding response resolvent modes. The quantified error is shown to be related to the time length of Welch blocks (spectral window size) normalised by a convective time. Subsequently, an algorithm based on a temporal data shift is devised to further improve SPOD convergence and is applied to the Ginzburg–Landau system. Next, its efficacy is demonstrated in a numerical database of a boundary layer subject to bypass transition. The proposed approach achieves substantial improvement in mode convergence with smaller spectral window sizes with respect to the standard method. Furthermore, SPOD modes display growing wall-normal and spanwise velocity components along the streamwise direction, a feature which had not yet been observed and is also predicted by a global resolvent calculation. The shifting algorithm for the SPOD opens the possibility for using the method on datasets with time series of moderate duration, often produced by large simulations.

Experimental base flow modification on a swept wing using plasma forcing

This work experimentally investigates plasma actuator (PA) forcing effects on the base flow and developing crossflow (CF) instabilities in a swept wing boundary layer. Spanwise-invariant plasma forcing near the leading edge is configured according to the base flow modification (BFM) strategy. A simplified predictive model is constructed by coupling an experimentally derived plasma body force and a linear stability theory and is used to infer the stability characteristics of the boundary layer subject to BFM. The base flow velocity is measured by stereo particle image velocimetry (PIV) at various PA operating conditions. Similarly, the developing CF instabilities, triggered through discrete roughness elements, are quantified by planar-PIV. The results demonstrate that a PA can reduce the boundary layer CF component, whereas the control authority shows a high dependence on the momentum coefficient. The dissimilar reduction between the streamline-aligned velocity and CF component leads to a local re-orientation of the base flow. Spanwise spectral analysis of the time-averaged flow indicates that stationary CF instabilities can be favorably manipulated whereas the BFM reduction effects depend on the corresponding initial amplitudes of stationary instabilities. An evident spanwise shift in the trajectory of stationary CF vortices is observed, which appears to result from the local alteration of the boundary layer stability due to the PA forcing. Despite the overall reduction in the amplitude of stationary CF instabilities, unsteady disturbances are found to be enhanced by the PA forcing. The current results shed light on the underlying principles of BFM-based PA operation in the context of laminar flow control.

Spatial Input–Output Analysis of Actuated Turbulent Boundary Layers

This paper develops a spatial input–output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. One-way spatial integration is used to reformulate the problem in terms of spatial evolution equations. The associated input-output operator is then used to examine the effect of localized periodic actuation at a given temporal frequency, based on an experimental setup in which an active large scale structure is introduced into the outer layer of a turbulent boundary layer. First, the large-scale structures associated with the phase-locked modal velocity field obtained from spatial input–output analysis are shown to closely match those computed based on hot-wire measurements. The approach is then used to further investigate the response of the boundary layer to the synthetically generated large-scale structures. A quadrant trajectory analysis indicates that the spatial input–output response produces shear stress distributions consistent with those in canonical wall-bounded turbulent flows in terms of both the order and types of events observed. The expected correspondence between the dominance of different quadrant behavior and actuation frequency is also observed. These results highlight the promise of a spatial input–output framework for analyzing the formation and streamwise evolution of structures in actuated wall-bounded turbulent flows.

Characterization of unsteady separation in a turbulent boundary layer: mean and phase-averaged flow

A spatially developing turbulent boundary layer subject to a space- and time-dependent pressure gradient is analysed via large-eddy simulation. The unsteadiness is prescribed by imposing an oscillating suction–blowing velocity profile at the top boundary of the computational domain. The alternating favourable and adverse pressure gradients cause the flow to separate and reattach to the wall periodically. A range of reduced frequencies $k$ was investigated, spanning from a very rapid flutter-like motion to a slow, quasi-steady flapping. The Reynolds number based on the boundary-layer displacement thickness $\delta _o^{*}$ at the inflow plane is $Re_*=1000$ . Both time- and phase-averaged fields are analysed and results are compared with steady conditions. The reduced frequency $k$ has a significant effect on the transient flow-separation process. For high $k$ the separation bubble does not grow as thick as in the corresponding steady case, but the length of the bubble remains comparable; hysteresis is observed in the near-wall region. As $k$ is reduced, a threshold is met at which the separation bubble grows in the wall-normal direction. However, the length of the bubble is significantly reduced again when compared with the steady case. At this frequency, the region of slow-moving fluid generated by the flow reversal is advected downstream, causing a decorrelation between the forcing (the imposed free-stream velocity) and the velocity and pressure downstream of the separation bubble. Moreover, hysteresis effects are shifted away from the wall. At the lowest frequency a quasi-steady solution is approached; however, transient effects are still present in the backflow region.

Localized drag modification in a laminar boundary layer subject to free-stream travelling waves via critical and Stokes layer interactions

Perturbation of the laminar boundary layer by free-stream travelling waves was shown to produce highly-localized skin friction modification via steady streaming. The forced boundary layer flow was calculated numerically and studied as a function of the phase speed, frequency and amplitude of the perturbations. Upstream-travelling waves always produced negative streaming, whereas downstream-travelling waves produced positive or negative streaming that varied with forcing strength and streamwise location. The sign of the resultant streaming was explained in terms of the inclination of the induced velocity modes, which evolved spatially in response to the streamwise variation and overlap of the Stokes and critical layers.

Transition in an infinite swept-wing boundary layer subject to surface roughness and free-stream turbulence

The instability of an incompressible boundary-layer flow over an infinite swept wing in the presence of disc-type roughness elements and free-stream turbulence (FST) has been investigated by means of direct numerical simulations. Our study corresponds to the experiments by Örlü et al. (Tech. Rep., KTH Royal Institute of Technology, 2021, http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291874). Here, different dimensions of the roughness elements and levels of FST have been considered. The aim of the present work is to investigate the experimentally observed sensitivity of the transition to the FST intensity. In the absence of FST, flow behind the roughness elements with a height above a certain value immediately undergoes transition to turbulence. Impulse–response analyses of the steady flow have been performed to identify the mechanism behind the observed flow instability. For subcritical roughness, the generated wave packet experiences a weak transient growth behind the roughness and then its amplitude decays as it is advected out of the computational domain. In the supercritical case, in which the flow transitions to turbulence, flow as expected exhibits an absolute instability. The presence of FST is found to have a significant impact on the transition behind the roughness, in particular in the case of a subcritical roughness height. For a height corresponding to a roughness Reynolds number $Re_{hh}=461$ , in the absence of FST the flow reaches a steady laminar state, while a very low FST intensity of $Tu =0.03\,\%$ causes the appearance of turbulence spots in the wake of the roughness. These randomly generated spots are advected out of the computational domain. For a higher FST level of $Tu=0.3\,\%$ , a turbulent wake is clearly visible behind the element, similar to that for the globally unstable case. The presented results confirm the experimental observations and explain the mechanisms behind the observed laminar–turbulent transition and its sensitivity to FST.

Input-output framework for actuated boundary layers

This work extends the input-output approach to the study of wall-bounded shear flows manipulated using actuators common in experimental flow control studies. In particular, we adapt this powerful analytical framework to investigate the flow response to specified geometric actuation patterns (e.g., different plasma actuators) that can be applied over a range of different temporal input signals. For example, the commonly studied steady-state (time-averaged) flow response corresponds to a superposition of step responses in our modeling framework. The approach takes advantage of the linearity of the transfer function representation to construct the actuated flow field as a weighted superposition of the flow responses to point sources of varying intensity comprising the actuation model. We first validate the proposed method through comparisons with numerical and experimental studies of the time-averaged behavior of a transitional boundary layer actuated using a dielectric-barrier discharge plasma actuator operating in constricted discharge mode. The method is shown to reproduce the streamwise velocity field and the vortical structures observed downstream from the tested plasma actuator configurations. We then demonstrate that the method provides even better agreement with the steady-state response of the boundary layer subject to actuation from arrays of symmetric plasma actuators arranged in both spanwise and serpentine geometries. These results indicate the utility of this extension to the widely used input-output framework in analyzing the effects of certain actuation modalities that have shown promise in flow manipulation strategies for drag reduction. An important benefit of this analytical method is the low computational cost associated with its use in extensive parametric studies that would be cost-prohibitive using experiments or high-fidelity simulations.

Insight into the dynamics of second grade hybrid radiative nanofluid flow within the boundary layer subject to Lorentz force

The magnetohydrodynamic hybrid second-grade nanofluid flow towards a stretching/shrinking sheet with thermal radiation is inspected in current work. Main concern of current investigation is to consider hybrid Al_{2} O_{3} - Cu nanofluid which is perceived by hanging two dissimilar kinds of nanoparticles known as alumina and copper within the base fluid. The fluid motion is produced by non-linear stretching/shrinking sheet. The modeled equations which comprise of energy, motion and continuity equations are changed into dimensionless form using group of similar variables. To determine the solution of transformed problem, the Homotopy Analysis technique is used. The findings of this work revealed that the magnetic parameter improves the heat transfer rate. This work also ensures that there are non-unique solutions of modeled problem for shrinking case and a unique solution for stretching case. Higher values of {text{Re}}_{x} results in declining of flow field. Rise in M agrees to a decline in velocity distributions. Higher values of second order fluid parameter reduces the viscosity of fluid and accordingly velocity increases. Velocity profile is also a decreasing function of volume friction.

Görtler vortices and streaks in boundary layer subject to pressure gradient: excitation by free stream vortical disturbances, nonlinear evolution and secondary instability

Abstract

Stability of the solitary wave boundary layer subject to finite-amplitude disturbances

The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output analysis, in which the environment noise is modelled as distributed body forces. The most dangerous perturbations in a time frame until flow reversal are found to be arranged as counter-rotating streamwise-constant rollers. One of these roller configurations is then selected and deployed to nonlinear equations, and streaks of various amplitudes are generated via lift-up mechanism. By means of secondary stability analysis and direct numerical simulations, the dual role of streaks in the boundary-layer transition is shown. When the amplitude of streaks remains moderate, these elongated features remain stable until the adverse-pressure-gradient stage and have a dampening effect on the instabilities developing thereafter. In contrast, when the low-speed streaks reach high amplitudes exceeding 15% of free-stream velocity at the respective phase, they become highly unstable to secondary sinuous modes in the outer shear layers. Consequently, a subcritical transition to turbulence, i.e., bypass transition, can be already initiated in the favourable-pressure-gradient region ahead of the wave crest.

Effects of favorable pressure gradient on turbulence structures and statistics of a flat-plate supersonic turbulent boundary layer

A Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a moderate favorable pressure gradient (FPG) induced by external expansion waves is investigated through direct numerical simulation and compared with a zero pressure gradient (ZPG) boundary layer. It is found that under FPG, the logarithmic region in the van Driest transformed velocity profile is lifted above the log law, while the wake region deviates below its ZPG counterpart. The near-wall streaks are elongated in the streamwise direction with wider spanwise spacing, which leads to an attenuated meandering effect compared to the ZPG case. Although small-scale motions in the outer layer are evidently suppressed, they survive mostly in the inner layer. On the other hand, large-scale motions tend to correlate further with the lifted fluid from upstream due to bulk dilatation. However, their relative locations within the boundary layer remain unchanged. Different responses of turbulence structures in the inner and the outer layer to FPG show that this two-layer feature within the boundary layer is mainly associated with the bulk dilatation rather than the wall curvatures. The profiles of turbulent kinetic energy (TKE) and turbulent Mach number also show a two-layer behavior, where the reduction in turbulence in the outer layer is more prominent than in the inner. Positive convection occurs from the buffer to the outer layer according to the TKE budget analysis, which compensates the production and resists the decrease in the turbulence level.

Bypass transition in a boundary layer subject to sheet-type freestream disturbance

Bypass transition in a boundary layer subject to sheet-type freestream disturbance

Direct numerical simulation of a supersonic turbulent boundary layer subject to adverse pressure gradient induced by external successive compression waves

A freestream Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a “pure” adverse pressure gradient (APG) without the impact of wall curvatures is studied by direct numerical simulation and compared with a benchmark flow with zero pressure gradient. Due to APG, the streamwise velocity shows an increase in the near-wall region and a reduction in the outer boundary layer. The principal strain rate shows a sandwich distribution along the wall-normal direction. The mismatch between the temperature and velocity fluctuations in both the inner and the outer layer is observed. Enhanced LSMs (large-scale motions) and large velocity patches are the typical flow structures in the outer and inner boundary layer subject to APG, respectively. From the analysis of quadrant decomposition, the sweep events dominate in the near-wall region while ejection events dominate the rest of the boundary layer. It is found that the baroclinicity plays a significant role in the formation of the enhanced LSMs in the outer boundary layer and the near-wall velocity patches. The resulting amplified vorticity further drives the interactive motions of the outer fluid and inner fluid. The turbulent kinetic energy and turbulent Mach number profiles are amplified by APG and a second peak is observed in both profiles. Turbulent energy budget analysis demonstrates that both the production and viscous effects are strengthened in the near-wall region while in the outer layer, the production is significantly amplified and balanced by the increased convection and turbulent transport.

On the stability of a Blasius boundary layer subject to localised suction

In this study the origins of premature transition due to oversuction in boundary layers are studied. An infinite row of circular suction pipes that are mounted at right angles to a flat plate subject to a Blasius boundary layer is considered. The interaction between the flow originating from neighbouring holes is weak and for the parameters investigated, the pipe is always found to be unsteady regardless of the state of the flow in the boundary layer. A stability analysis reveals that the appearance of boundary layer transition can be associated with a linear instability in the form of two unstable eigenmodes inside the pipe that have weak tails, which extend into the boundary layer. Through an energy budget and a structural sensitivity analysis, the origin of this flow instability is traced to the structures developing inside the pipe near the pipe junction. Although the amplitudes of the modes in the boundary layer are orders of magnitude smaller than the corresponding amplitudes inside the pipe, a Koopman analysis of the data gathered from a nonlinear direct numerical simulation confirms that it is precisely these disturbances that are responsible for transition to turbulence in the boundary layer due to oversuction.

Recovery of the inherent dynamics of noise-driven amplifier flows

Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbations. A dynamic mode decomposition performed with snapshots taken in the statistically steady state extracts marginally stable dynamic modes, which mimic the sustained dynamics but miss the actual intrinsic stable behaviour of these flows. In this study, we present an alternative data-driven technique which attempts to identify and separate the intrinsic linear stable behaviour from the driving term. This technique uses a system-identification algorithm to extract a reduced state-space model of the flow from time-dependent input–output data. Such a model accurately predicts the values of the velocity field (output) from measurements of an upstream sensor that captures the effect of the incoming perturbations (input). The methodology is illustrated on a two-dimensional boundary layer subject to Tollmien–Schlichting instabilities, a canonical example of flow acting as a noise amplifier. The spectrum of the identified model compares well with the results reported in literature for the full-order system. Yet the comparison appears to be only qualitative, due to the poor robustness properties of eigenvalue spectra in noise-amplifier flows. We therefore advocate the use of the frequency response between the upstream sensor and the flow dynamics, which is revealed to be a robust quantity. The frequency response is validated against full-order computations and compares well with a local spatial stability analysis.

A new method for measuring turbulent heat fluxes using PIV and fast-response cold-wires

A new method for measuring turbulent heat fluxes using a combination of particle image velocimetry and a nanoscale fast-response cold-wire is tested by examining a rough-wall turbulent boundary layer subject to weakly stable stratification. The method has the advantages of simple calibration and setup, as well as providing spatial correlations of velocity and temperature and their associated integral length scales. The accuracy of using Taylor’s hypothesis when employing a large field of view is investigated. Heat flux, velocity–temperature correlation coefficients and turbulent Prandtl number profiles, as well as spatial velocity and temperature correlations, are presented.

Stability of the laminar boundary-layer flow behind a roughness element

Roughness elements in laminar boundary layers generate both high shear layers and streaky structures. Because these phenomena interact, it is difficult to precisely ascertain the dominant instability mechanisms. With the goal of explicating such interactions, we study the stability of a laminar boundary layer subject to a single roughness element at a Reynolds number subcritical of bypass transition. Our work involves two parts: bi-global linear stability theory (LST) analysis and corroborating experimental measurements. Linear stability analysis of a flat-plate boundary layer perturbed by streamwise streaks reveals the presence of several unstable modes. Of the dominant two modes, one exhibits spanwise symmetry and the other is antisymmetric. These modes are termed ‘varicose’ and ‘sinuous,’ respectively. Corroborating experiments were conducted in the laminar water channel of the University of Stuttgart. By simultaneously traversing two hot-film probes, we are able to confirm the presence of both eigenmodes predicted by LST and to extract relevant data for each: eigenvalues, eigenfunctions, growth rates and phase distributions. The main part of the experiments has been performed under ‘natural’ conditions, i.e., in the absence of external forcing. As the amplitude of the sinuous part of the results is much smaller than the varicose one and hence affected by measurement noise, a case with asymmetric external forcing is presented as well. Despite some deficiencies of the setup, it is possible to enhance the sinuous mode with respect to the unforced case and to confirm its existence as an eigenmode of the flow.