Flat Plate Boundary Layer Research Articles

Effect of Local Thermal Strips on Hypersonic Boundary-Layer Instability

An effect of localized thermal strips on hypersonic boundary-layer instability is investigated using linear stability theory (LST). The linear evolution of Mack's second mode is analyzed for a Mach 4.5 flat-plate boundary-layer with and without the strips. The validity of the LST analysis is assessed through the comparison of the results with implicit large eddy simulations (ILES) for selected cases. Parametric studies on the temperature intensity, length, and location of a single strip are performed to examine the influence of the strip on the second-mode instability. A reversal in the stabilizing and destabilizing effect according to the local streamwise surface pressure gradient induced by the strip is identified. The reversal point of the stabilizing/destabilizing effect is located in the vicinity of the location of the maximum growth rate of the second mode. The influence of three strips in a series arrangement is also analyzed for several combinations. The proper combination of strips, considering the reversal phenomenon, results in more significant stabilizing/destabilizing effects for a disturbance with a specific frequency. The overall effects are also evaluated and analyzed in terms of the envelope of the N-factor curves by carrying out the LST calculations for disturbances with various frequencies.

Three-dimensional wall heating elements effect on the instability in zero pressure gradient supersonic boundary layers

The streaky boundary layers have very important roles in laminar-turbulent transition. Streaks of appropriate size can influence stabilities in boundary layers. In this paper, the effect of steady streamwise elongated, spanwise periodic wall heating elements on the first mode instability in supersonic flat plate boundary layers was investigated. For the balance of the efficient and accuracy, the linearized Navier–Stokes equations are used to obtain the base flow and compared with compressible Navier–Stokes equations. A bi-global analysis tool is used for the instability analysis because the heating source has a much larger length-scale in the streamwise direction than that in the spanwise direction, and the streamwise velocity is much larger than the normal velocity and the spanwise one. Results indicated that the distortion caused by the three-dimensional surface heating elements could modify the first mode, resulting in a lower frequency but with an uncertain effect on the higher frequency modes. Additionally, the streaks make the lower spanwise wave number components of the even first mode disturbance in a three-dimensional supersonic boundary layer in the freestream. As a result, the spontaneous radiation of an acoustic wave to the far field was found for the even mode. These findings suggest that laminar-turbulence transition can be suppressed or enhanced by the three-dimensional wall heating.

Active transition control by synthetic jets in a hypersonic boundary layer

We investigate by direct numerical simulation the active control of laminar-turbulent transition in a hypersonic flat-plate boundary layer at a freestream Mach number of 5.86. The control mechanism is a synthetic jet. Based upon the linear stability theory of Mack, in hypersonic flow the important path to transition involves a high-frequency, second-mode fundamental resonance. Through systematic investigation, we reveal that the forcing the boundary layer with a synthetic jet at appropriate combinations of amplitude and frequency suppresses the second mode and delays transition. To gain physical insights into the major control mechanism, we employ the momentum potential theory (MPT) to analyze the flows with and without control. Essentially, the underlying control mechanism relies on an intriguing effect of the synthetic jet via generating the outward radiated wave structures, which are identified to split the upstream acoustic and vortical components. The splitting treatment presents the second-mode energy to drop sharply after the flow passes through the synthetic jet slot. The MPT source-term analysis reveals that the significantly suppressed near-wall source terms are responsible for suppressing the second mode downstream. Compared with the vortical and thermal source terms, the acoustic source term is found to be suppressed most. The kinetic budget analysis further reveals that the splitting treatment is related to the non-parallel effect and the nonlinear interaction.

Data-driven framework for input/output lookup tables reduction: Application to hypersonic flows in chemical nonequilibrium

In this paper, we present a novel model-agnostic machine learning technique to extract a reduced thermochemical model for reacting hypersonic flows simulation. A first simulation gathers all relevant thermodynamic states and the corresponding gas properties via a given model. The states are embedded in a low-dimensional space and clustered to identify regions with different levels of thermochemical (non)-equilibrium. Then, a surrogate surface from the reduced cluster-space to the output space is generated using radial-basis-function networks. The method is validated and benchmarked on a simulation of a hypersonic flat-plate boundary layer with finite-rate chemistry. The gas properties of the reactive air mixture are initially modeled using the open-source Mutation++ library. Substituting Mutation++ with the light-weight, machine-learned alternative improves the performance of the solver by 50% while maintaining overall accuracy.

Turbulent boundary layer control with DBD plasma actuators

The flat-plate turbulent boundary layer at Re τ = 1140 is manipulated using a spanwise array of bidirectional dielectric barrier discharge (DBD) plasma actuators. Based on the features of no moving mechanical parts in the DBD plasma control technology and hot-wire anemometer velocity measurements, a novel convenient method of local drag reduction (DR) measurement is proposed by measuring the single-point velocity within the linear region of the viscous sublayer. We analyze the premise of using the method, and the maximum effective measurement range of −73.1% < DR < 42.2% is obtained according to the experimental environment in this work. The local drag decreases downstream of the center of two adjacent upper electrodes and increases downstream of the upper electrodes. The magnitude of the local DR increases with increasing voltage and decreases as it moves away from the actuators. For the spanwise position in between, the streamwise distribution of the local DR is very dependent on the voltage. The variable-interval time-average detection results reveal that all bursting intensities are reduced compared to the baseline, and the amount of reduction is comparable to the absolute values of the local DR. Compared with previous results, we infer that the control mechanism is that many meandering streaks are combined together into single stabilized streaks.

Global receptivity analysis: physically realizable input–output analysis

In the context of transition analysis, linear input–output analysis determines the worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with direct numerical simulations of a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.

Delay of laminar–turbulent transition by counter-rotating cylindrical roughness elements in a laminar flat plate boundary layer

Delaying laminar–turbulent transition in boundary layers is of great interest since the skin-friction coefficient can be reduced by up to one order of magnitude. In this experimental research, it is shown that counter-rotating cylindrical roughness elements are able to delay transition under realistic flow conditions. Evidence is given by the intermittency, evaluated from hot-film measurements in a laminar water channel. An increase in rotation speed results in a delay of transition of up to {6.5}{%} in the center of the plate. This trend can be explained by the streaks amplified by the rotating cylinders, resulting in a damping of the fluctuation amplitude in the boundary layer. The advantage of this method is that the transition delay can be actively controlled with conventional cylindrical roughness elements.Graphical abstract

DNS Study on Turbulent Transition Induced by an Interaction between Freestream Turbulence and Cylindrical Roughness in Swept Flat-Plate Boundary Layer

Laminar-to-turbulent transition in a swept flat-plate boundary layer is caused by the breakdown of the crossflow vortex via high-frequency secondary instability and is promoted by the wall-surface roughness and the freestream turbulence (FST). Although the FST is characterized by its intensity and wavelength, it is not clear how the wavelength affects turbulent transitions and interacts with the roughness-induced transition. The wavelength of the FST depends on the wind tunnel or in-flight conditions, and its arbitrary control is practically difficult in experiments. By means of direct numerical simulation, we performed a parametric study on the interaction between the roughness-induced disturbance and FST in the Falkner–Skan–Cooke boundary layer. One of our aims is to determine the critical roughness height and its dependence on the turbulent intensity and peak wavelength of FST. We found a suppression and promotion in the transition process as a result of the interaction. In particular, the immediate transition behind the roughness was delayed by the long-wavelength FST, where the presence of FST suppressed the high-frequency disturbance emanating from the roughness edge. Even below the criticality, the short-wavelength FST promoted a secondary instability in the form of the hairpin vortex and triggered an early transition before the crossflow-vortex breakdown with the finger vortex. Thresholds for the FST wavelengths that promote or suppress the early transition were also discussed to provide a practically important indicator in the prediction and control of turbulent transitions due to FST and/or roughness on the swept wing.

Reinforcement-learning-based control of convectively unstable flows

This work reports the application of a model-free deep reinforcement learning (DRL) based flow control strategy to suppress perturbations evolving in the one-dimensional linearised Kuramoto–Sivashinsky (KS) equation and two-dimensional boundary layer flows. The former is commonly used to model the disturbance developing in flat-plate boundary layer flows. These flow systems are convectively unstable, being able to amplify the upstream disturbance, and are thus difficult to control. The control action is implemented through a volumetric force at a fixed position, and the control performance is evaluated by the reduction of perturbation amplitude downstream. We first demonstrate the effectiveness of the DRL-based control in the KS system subjected to a random upstream noise. The amplitude of perturbation monitored downstream is reduced significantly, and the learnt policy is shown to be robust to both measurement and external noise. One of our focuses is to place sensors optimally in the DRL control using the gradient-free particle swarm optimisation algorithm. After the optimisation process for different numbers of sensors, a specific eight-sensor placement is found to yield the best control performance. The optimised sensor placement in the KS equation is applied directly to control two-dimensional Blasius boundary layer flows, and can efficiently reduce the downstream perturbation energy. Via flow analyses, the control mechanism found by DRL is the opposition control. Besides, it is found that when the flow instability information is embedded in the reward function of DRL to penalise the instability, the control performance can be further improved in this convectively unstable flow.

Experimental investigation of the dynamic characteristics of the flow generated by a sliding dielectric barrier discharge in the flat plate boundary layer flow

The sliding dielectric barrier discharge (SL-DBD) has attracted attention due to its ability to suppress flow separation. This paper investigated the effect of SL-DBD on the flow field in the flat plate boundary layer by time-resolved particle image velocimetry. We obtained the finite-time Lyapunov exponent field and the Lagrangian coherent structures of the flow field through the velocity field. The results show the effect of SL-DBD has spatial differences, and SL-DBD will produce a “strong–weak–strong” spatial effect on the flow field. The directionality of the flow structure induced by SL-DBD is the main reason for the difference. SL-DBD will induce a large number of vortex structures in the local downstream area of the electrode. The vortex structure enhances the mixing and squeezing effects between the upper and lower flow fields. The upper flow field moves the lower flow field downward by about 0.1 mm through the squeezing effect. In addition, at the downstream region adjacent to the electrode, the oblique momentum injection of the SL-DBD is the dominant effect. At one electrode distance from the electrode, the SL-DBD induces a large number of vortex structures. However, when the distance from the electrode is twice the electrode spacing, the number of vortex structures decreases, and the structure becomes larger. The results show spatial differences in the perturbation of the flow field by SL-DBD, which cannot be ignored when SL-DBD is used to suppress flow separation.

Critical Transition Reynolds Number for the Incompressible Flat-Plate Boundary Layer as Searched by Numerical Simulation

Critical Transition Reynolds Number for the Incompressible Flat-Plate Boundary Layer as Searched by Numerical Simulation

Wall-Modeled Large-Eddy Simulation with Second-Order-Accurate Upwind Scheme

In aircraft aerodynamic design, it is essential for certification by analysis to estimate aircraft aerodynamic characteristics with high fidelity across the full flight envelope using computational fluid dynamics. Improving accuracy of the simulation of unsteady flows such as transonic buffet is one of the problems. Wall-modeled large-eddy simulation (WMLES) is expected to improve the accuracy. In this study, three quantitative requirements for the matching points, where LES feeds the wall model with flow variables, are proposed to ensure the accuracy of the WMLES with a second-order-accurate upwind scheme that is often used for engineering codes. These requirements are related to 1) matching point height, 2) the number of cells below the matching point, and 3) grid resolution at the matching point. The proposed requirements are assessed on a flat-plate turbulent boundary layer and a shock/turbulent boundary-layer interaction flow. As a result, it is clarified that all of the requirements are necessary to ensure the accuracy in terms of mean velocity, Reynolds stresses, and skin friction.

Flat plate boundary layer accelerated by shock wave propagation

The flat plate transitional boundary layer response to the acceleration induced by the shock wave propagation is studied using large-eddy simulations. The steady boundary layer global behaviour is first investigated before focusing on the transient response of a turbulent region following the shock wave propagation. It is shown that the transient response of the turbulent region exhibits strong similarities with the spatial transition process to turbulence induced by free-stream turbulence, the so-called bypass transition. The boundary layer does not evolve gradually from the initial turbulence intensity to the final turbulence intensity but undergoes a temporal transition process composed of three distinct phases. These three different phases are comparable with the three stages of a bypass transition (i.e. buffeted laminar flow, transition and fully turbulent) because they are governed by the same physical processes. On the other hand, it is highlighted that this temporal response is identical to that described by He &amp; Seddighi (J. Fluid Mech., vol. 715, 2013, pp. 60–102) during the study of an incompressible boundary layer undergoing an increase of mass flow rate. The boundary layer compression by the shock propagation does not contribute to any significant change in the turbulence dynamic after an unsteady acceleration.

Impact of Wall Temperature on Aerothermal Characteristics of an Array of Surface Microstructures

Abstract The aero-thermal behavior of surface microstructures is of wide relevance, especially given the development of additive manufacturing (AM). Of particular interest is the interaction between fluid flow and heat transfer. In this work, two contrasting configurations, a flat plate boundary layer and an array of hemispheric microstructures are examined at three wall-inflow temperature ratios (TR): cooled (TR = 0.5), adiabatic (TR = 1) and heated wall (TR = 1.5). Due to compensation between fluid viscosity and velocity gradient in the boundary layer, the heat transfer effects may appear deceptively small if judged using the common aerothermal parameters (Cf, Nu). The authors find instead the local Reynolds number to be more usefully indicative of such aerothermal interaction. The scale-resolving large eddy simulations (LES) simulations at a range of Reynolds numbers show that the cooled wall case is characterized by a markedly earlier transition which takes place at a much lower (by 50%) bulk flow Reynolds number compared to a near-adiabatic case. Furthermore, it is shown that the incompressible flow LES solutions fail to capture the early transition under the same cooling condition. Finally, a regrouping of the nondimensional parameters (CD, Nu) with TR is proposed leading to a more unified characterization for easier scaling of wall heat transfer effects in practical applications.

Time-resolved visualization of coherent structures during supersonic boundary layer transition

The coherent structures arising during flat-plate boundary layer transition at Mach number 3.4 are investigated using a custom-built hyper-rate imaging system. The evolution of transitional structures is investigated in the Eulerian and Lagrangian reference frames. The upstream evolution of transition is dominated by the generation of new hairpin structures, while the interaction among multiple structural types dominates the evolution downstream. The breakdown of the existing structure, which may be caused by interactions among multiple types of structures with similar scales, is also visualized.

A comparative study of experiments with numerical simulations of free-stream turbulence transition

To date, very few careful and direct comparisons between experiments and direct numerical simulations (DNS) have been published on free-stream turbulence (FST) induced boundary layer transition, whilst there exist numerous published works on the comparison of canonical turbulent boundary layers. The primary reason is that the former comparison is vastly more difficult to carry out simply because all known transition scenarios have large energy gradients and are extremely sensitive to surrounding conditions. This paper presents a detailed comparison between new experiments and available DNS data of the complex FST transition scenario in a flat plate boundary layer at turbulence intensity level about $Tu = 3\,\%$ and FST Reynolds number about $Re_{{fst}} = 67$ . The leading edge (LE) pressure gradient distribution and the full energy spectrum at the LE are identified as the two most important parameters for a satisfying comparison. Matching the LE characteristic FST parameters is not enough as previously thought, which is illustrated by setting up two experimental FST cases with about the same FST integral parameters at the LE but with different energy spectra. Finally, an FST boundary layer penetration depth (PD) measure is defined using DNS, which suggests that the PD grows with the downstream distance and stays around 20 % of the boundary layer thickness down to transition onset. With this result, one cannot rule out the significance of the continuous FST forcing along the boundary layer edge in this transition scenario, as indicated in previous studies.

Assessment of implicit LES modelling for bypass transition of a boundary layer

The implicit LES model recently introduced by Dairay et al. (2017), which is based on numerical dissipation introduced via the discretisation of the viscous term, is assessed for the case of a flat plate boundary layer submitted to external turbulence and undergoing bypass transition. The free stream turbulent fluctuations are generated using a recently proposed linear forcing method adapted to control their intensity and length scale. Two configurations are considered, one with the leading edge of the plate taken into account and one without. LES results for the configuration without leading edge are compared with a DNS, and results for the configuration with leading edge are compared with available experimental and numerical reference data from the literature. Global parameters, unconditional and conditional statistics, as well as Reynolds stress budgets are analysed, and good agreements are obtained with reference data, hence confirming the ability of the model to predict accurately transitional flows. In particular, it is shown that, thanks to its action limited to the smallest resolved scales, the model is only active in the transitional and turbulent regions and therefore does not alter the development of the streaks in the laminar region of the boundary layer.

Analysis of a higher-order vorticity confinement scheme in flux correction form

This article presents a detailed comparison of the classical source-term formulation of higher-order Vorticity Confinement with a flux-correction version, through an application to a series of well-documented cases. Both formulations and their numerical implementation are presented first. Then the methods are applied to the simple case of the long-time advection of an inviscid and isentropic vortex. A shock-vortex interaction case is also computed to demonstrate the compatibility of the method with the shock-capturing properties of the baseline scheme. Both methods are finally applied to a ZDES mode 3 (Wall-Modelled LES) simulation of a zero-pressure-gradient flat-plate turbulent boundary layer, showing a better preservation of smaller-scale vortical structures with respect to standard higher-order numerical schemes. Furthermore, the flux-correction form of Vorticity Confinement significantly improves the prediction of skin friction with respect to both the baseline scheme and the classical source-term formulation, thus showing that the flux-correction form of confinement is essential for a reliable prediction of this quantity.

Visibility analysis of boundary layer transition

We study the transition to turbulence in a flat plate boundary layer by means of visibility analysis of velocity time-series extracted across the flow domain. By taking into account the mutual visibility of sampled values, visibility graphs are constructed from each time series. The latter are, thus, transformed into a geometrical object, whose main features can be explored using measures typical of network science that provide a reduced order representation of the underlying flow properties. Using these metrics, we observe the evolution of the flow from laminarity to turbulence and the effects exerted by the free-stream turbulence. Different from other methods requiring an extensive amount of spatiotemporal data (e.g., full velocity field) or a set of parameters and thresholds arbitrarily chosen by the user, the present network-based approach is able to identify the onset markers for transition by means of the streamwise velocity time-series alone.

New Insights into Turbulent Spots

Transitional–turbulent spots bridge the deterministic laminar state with the stochastic turbulent state and affect the transition zone length in engineering flows. Turbulent spot research over the past four decades has expanded from incompressible flat-plate boundary layer and pipe flow to hypersonic boundary layer flow, turbomachinery flow, channel flow, plane Couette flow, and a range of more complex flows. Progress has been made on the origination, composition, demarcation, growth, mutual interaction, reproduction, sustainability, and self-organization of turbulent spots. The hypothesis that transitional–turbulent spots are a basic module of the fully turbulent boundary layer has been proven through the discovery of locally generated turbulent–turbulent spots dominating the wall layer. Splitting of transitional–turbulent spots in pipe flow has been linked to a life cycle localized in the spot frontal section. This review discusses these advances and outlines future research directions.