Flat Plate Boundary Layer Research Articles

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.

Time-frequency analysis for two cases of boundary-layer transition induced by random distributed roughness

The boundary layer transition induced by distributed surface roughness has great practical relevance, but remains poorly understood. In this experimental work, we investigate the transition in a flat-plate boundary layer downstream of a localized strip of random distributed roughness. The boundary layer exhibits different temporal and spectral behaviour in two (roughness-) Reynolds-number regimes separated by a critical value. In the “sub-critical” regime, the velocity signals show presence of “turbulent spots”, whereas in the “super-critical” regime, no distinct turbulent spots are observed. Two boundary-layer profiles, one each from the sub-critical and super-critical regimes, are chosen for comparison. The sub-critical case exhibits a bi-modal power spectrum having two humps in frequency ranges differing by an order of magnitude, whereas the super-critical case has a uni-modal spectrum with a single hump in the high-frequency range. The wavelet analysis shows that the energy distribution is intermittent in time for both the cases at all frequencies. However, for the sub-critical case, the energy in the high-frequency range appears as clusters, which are seen as turbulent spots in the velocity signal. On the other hand, for the super-critical case there is no such clustering, consistent with the absence of spots in the velocity signal. We conjecture that, for the sub-critical case, the motions corresponding to the low-frequency spectral hump (possibly the streamwise streaks) could be responsible for imparting organization to the high-frequency motions in the form of turbulent spots. We also detect “events” in the wavelet-energy time series. For the sub-critical case, the events in the high-frequency range have a higher degree of time-localization, which increases with frequency. For the super-critical case, however, the time-localization is independent of frequency over nearly the entire frequency range. These findings present two different scenarios for the late stages of transition, having distinct time-frequency behaviour. This could have implications towards modelling roughness-induced transition.

Negative skin friction during transition in a zero-pressure-gradient flat-plate boundary layer and in pipe flows with slip and no-slip boundary conditions

In searching for the mechanisms of boundary layer bypass transition, Schubauer & Klebanoff (NACA-TR-1289, 1956) conducted an extensive search for negative skin-friction events during the laminar-to-turbulent transition in a zero-pressure-gradient, smooth flat-plate boundary layer (ZPGSFPBL) under a wide range of free-stream turbulence intensity levels. They concluded that no evidence of incipient flow separation could be found in any part of the transition region. Although it has been known that extremely rare backflow events can occur in a fully turbulent ZPGSFPBL and in fully developed turbulent pipe flow, the Schubauer–Klebanoff conclusion regarding the total absence of negative skin friction in ZPGSFPBL transition has remained unchallenged over the past six decades. Here we report our discovery of negative skin-friction events during the bypass transition in an extensively researched representative ZPGSFPBL case, and in pipe flows with no-slip and slip boundary conditions under circumferential mode inlet disturbance, respectively. The peak probability of such events is located in the late stage of transition between the streamwise stations where the minimum and maximum mean skin friction are attained. The magnitude of the peak probability is substantially larger than the corresponding probability in the downstream fully turbulent region: in the case of no-slip pipe flow, the difference is two orders of magnitude and is primarily due to an enhanced number density of the backflow events coupled with a notable increase in the wall footprint size of such events. For both the boundary layer and pipe flows considered here, and in both the transitional and fully turbulent regions, the incipient negative skin friction is found, through instantaneous flow visualization and conditional averaging, to be induced by the head element of a reverse hairpin vortex.

Experimental study on supersonic plate boundary layer transition under pulsed arc plasma excitation control

Pulsed arc plasma excitation is characterized by strong local heating effect and wide disturbance range, and it has a broad application prospect in supersonic flow control. In this paper, by using electrical parameter measurement system and high speed schlieren technique, we study the electrical and flow field characteristics of pulsed arc plasma excitation under the condition of <i>Ma</i> = 3 incoming flow. The nano-particle planar laser scattering (NPLS) is used to investigate the flow structure of the supersonic flat boundary layer, and the transition characteristics of the boundary layer at different plasma excitation frequencies are studied. The experimental results show that in the flow field with <i>Ma</i> = 3 and the total incoming pressure <i>P</i><sub>0</sub> = 1 atm (1 atm = 1.01 × 10<sup>5</sup> Pa), the peak voltage of the pulsed arc plasma actuator discharge is 6 kV, the peak current is 70 A, the time scale of the discharge is about 300 ns, the single discharge energy is 70 mJ; the pulsed arc discharge will produce the precursor shock wave with higher velocity and the thermal deposition zone with higher temperature, which will exert continuously disturbance on the boundary layer. The pulsed arc plasma excitation with perturbation can promote the transition of supersonic plate boundary layer. Moreover, the high-frequency impact effect of pulsed discharge can promote the transition to occur ahead of time, and the higher the frequency, the better the effect is. As the excitation frequency increases, the transition position of the boundary layer of the supersonic flat plate moves forward, and the length of the transition area of the boundary layer becomes shorter as the excitation frequency increases. When the excitation frequency is 60 kHz, the length of transition zone is 0 and the thickness of turbulent boundary layer is 25 mm. When a high frequency is applied (<i>f</i> = 40, 60 kHz), the transition path of the boundary layer is that the shock wave generated by the plasma excitation triggers the unstable wave, and the development of unstable waves directly skips the linear growth stage, passes through the bypass and transitions into turbulent flow. The pulsed arc plasma excitation can be used to promote supersonic boundary layer transition.

Effect of Computational Domain on Numerical Simulation of Flat-Plate Boundary Layer with OpenFOAM

Effect of Computational Domain on Numerical Simulation of Flat-Plate Boundary Layer with OpenFOAM

Experimental study on effect of transverse groove with/without discharge hole on hypersonic blunt flat-plate boundary layer transition

Experiments are carried out on the <i>Φ</i>2 m Shock Tunnel (FD-14A) at the China Aerodynamics Research and Development Center to study the effect of the transverse groove with/without discharge hole on the hypersonic blunt flat-plate boundary layer transition, and the preliminary computational and theoretical research are carried out. The inflow Mach number of the test is 6, the unit Reynolds number is 3.3 × 10<sup>7</sup>/m, the leading edge radius of the flat-plate is 1 mm, and the angle of attack is –4°. Three different sets of two-dimensional transverse grooves are arranged at 110 mm away from the leading edge of the flat-plate. The width and depth of the grooves are, respectively, 2.5 mm and 1 mm for groove 1, 3.75 mm and 1.5 mm for groove 2, and 5 mm and 2 mm for groove 3, at the same time, both ends of the groove 1 can open the discharge hole (the discharge hole has a size of 2.5 mm × 5.0 mm and a width the same as that of groove 1). The discharge hole is denoted as the groove 4, and the smooth flat-plate when the groove is not included is denoted as groove 5 or the flat. The <i>Φ</i>2-mm-diameter cylindrical heat flux sensor is used to measure the heat flux distributions of the center line of the flat-plate under different conditions, and thus we can judge the transition of the boundary layer. The measurement results show that the smooth plate starts to transit at <i>x</i> ≈ 340 mm, and the transition is nearly completed at <i>x</i> ≈ 425 mm. The groove causes the transition position of the boundary layer of the plate to advance, and as the width and depth of the groove increase, the promoting effect on the transition is enhanced, and the transition position moves upstream. After the groove 1 is added to the discharge hole (groove 4), the heat flux distribution and the transition position are substantially the same as those of the smooth plate. After the boundary layer flow completely transits into turbulent flow, the difference in heat flux for each case is small, which indicates that the grooves of different specifications affect only the heat flux distribution in the transition process, but have little effect on the heat flux of the turbulent wall after the transition. The computational fluid dynamic results show that the discharge holes cause passive suction, and the test results show that the suction effect of the discharge holes at both ends of the groove counteracts the effect of the groove on the transition of the center line boundary layer, but it may be just a coincidence, and further research is needed. The linear stability theory (LST) and the optimal perturbation method are used to analyze the flow instability mechanism of the smooth blunt plate. The LST results show that there is no first mode instability nor second mode instability in the blunt plate flow. The modal instability mechanism cannot explain the observed transition in the test. The optimal disturbance calculation shows that the blunt plate flow suffers strong non-modal instability, which can qualitatively explain the observed transition phenomenon.

Устойчивость сверхзвукового пограничного слоя на сублимирующей поверхности

Theoretical investigation of the supersonic flat-plate boundary-layer properties under conditions of the surface material sublimation has been performed for Mach number M = 2. Naphthalene (C10H8) was chosen as the substance for the sublimation coating. Performed computations show that with increasing surface temperature due to stagnation temperature increase, the mass flow rate of naphthalene evaporation increases. Calculations performed on the basis of linear stability theory show that such an increase of evaporation leads to a noticeable decrease of the local growth rates of unstable perturbations in the boundary layer. It is found that stabilization of the boundary layer by the surface coating sublimation occurs with increasing temperature of the sublimation coating, reaching a maximum near the triple point temperature of the sublimation material. The carried out experiments confirmed the stabilizing effect of surface sublimation.

Wavelet-Based Adaptive Unsteady Reynolds-Averaged Navier–Stokes Simulations of Wall-Bounded Compressible Turbulent Flows

A wavelet-based adaptive approach, called wavelet-based adaptive unsteady Reynolds-averaged Navier–Stokes (WA-URANS), is proposed to solve the URANS equations for the computation of wall-bounded internal and external compressible turbulent flows. The new approach uses anisotropic wavelet-based mesh refinement, and its effectiveness is demonstrated for flow simulations with two different turbulence models, namely, the Spalart–Allmaras and models for a variety of two- and three-dimensional flow configurations with arbitrary geometries, different speed regimes, and various boundary conditions. Supersonic plane channel flow, a weakly compressible channel flow with periodic hill constrictions, a subsonic zero-pressure-gradient flat-plate boundary-layer flow, the separated flow over NASA wall-mounted hump, the Bachalo–Johnson flow (axisymmetric transonic bump flow), and a flow past a circular cylinder at a subcritical Reynolds number are tested as benchmark flows. The effectiveness and efficiency of the new wavelet-based approach are demonstrated by comparing the results of the WA-URANS simulations with literature data. This comprehensive validation of the WA-URANS approach encourages its application to practical problems of industrial interest, and demonstrates the feasibility of extending this approach to wavelet-based wall-modeled large-eddy simulation (LES) and hybrid URANS/LES. Finally, the current study serves as a baseline for the development of a unified hierarchical framework for eddy-resolving turbulence modeling, capable of performing computations of different fidelity, ranging from adaptive direct numerical simulations to adaptive URANS computations.

Implicit Discontinuous Galerkin Solution on Unstructured Mesh for Turbine Blade Secondary Flow

Abstract To enhance solution accuracy with high-order methods, an implicit solver using the discontinuous Galerkin (DG) discretization on unstructured mesh has been developed. The DG scheme is favored chiefly due to its distinctive feature of achieving a higher-order accuracy by simple internal sub-divisions of a given mesh cell. It can thus relieve the burden of mesh generation for local refinement. The developed method has been assessed in several test cases. First, an examination on the mesh-dependency with different DG orders for discretization has demonstrated the expected mesh convergence order of accuracy correlation. The flow around a cylinder solved with up to the fifth-order accuracy demonstrates the need for a high-order geometrical representation corresponding to the high-order flow field discretization. A calculated turbulent flat plate boundary layer demonstrates the capability of the high-order DG in capturing the laminar sub-layer for a given coarse mesh (y + >20) without a wall function, in a clear contrast to a conventional second-order scheme. The focal test case of the present work is a high-pressure (HP) turbine cascade with the flow losses being strongly influenced by both the laminar separation induced transition on the blade suction surface and the secondary flow development in the endwall region. Fully turbulent RANS solutions consistently overpredict the losses, which can be significantly reduced by an empirically specified transition at a mid-chord point. Of particular interest is a contrasting behavior of pure laminar flow solutions. A steady laminar flow solution is difficult to converge, and even when converging, tends to give an unrealistically large separation. On the other hand when the laminar solution is run in a time-accurate unsteady mode, a qualitatively different flow pattern emerges. The separated shear layer is then shown to lead to coherently shed unsteady vortices with a net entrainment from the main stream to the near-wall region. The resultant time-averaged near-wall flow then effectively becomes a reattached boundary layer. Both overall and distributed losses computed from unsteady laminar solutions are shown to be consistently much better than the fully turbulent RANS solutions. It is remarkable and quite unexpected that for such a seemingly complex 3D flow problem, the straightforward unsteady laminar solutions with no empirical input seem to be comparable with (or slightly better than) the tripped RANS with empirical input.

Supersonic boundary layer transition induced by self-sustaining dual jets**Project supported by the National Natural Science Foundation of China (Grant Nos. 11602299, 11872374, and 51809271).

To promote high-speed boundary layer transition, this paper proposes an active self-sustaining dual jets (SDJ) actuator utilizing the energy of supersonic mainflow. Employing the nanoparticle-based planar laser scattering (NPLS), supersonic flat-plate boundary layer transition induced by SDJ is experimentally investigated in an Ma-2.95 low-turbulence wind tunnel. Streamwise and spanwise NPLS images are obtained to analyze fine flow structures of the whole transition process. The results reveal the transition control mechanisms that on the one hand, the jet-induced shear layer produces unstable Kelvin–Helmholtz instabilities in the wake flow, on the other hand, the jets also generates an adverse pressure gradient in the boundary layer and induce unstable streak structures, which gradually break down into turbulence downstream. The paper provides a new method for transition control of high-speed boundary layer, and have prospect both in theory and engineering application.

A rational method for determining intermittency in the transitional boundary layer

A new rational procedure is proposed for determining the intermittency in the streamwise direction. One of the key parameters for the intermittency determination is the selection of a threshold value, which often involves a certain level of subjectivity. Here, a reliable way of choosing the threshold value in a more objective manner is proposed. The proposed approach involves a single threshold value, equal to the magnitude of the maximum laminar perturbation in the transitional flow. The results obtained are validated with the widely used dual-slope method. In this paper, the measurements are carried out on an experimental arrangement, involving the interaction of an upstream aerofoil wake with a downstream flat plate boundary layer. As a by-product of the study, a scaling parameter has been identified which captures the length of the transition zone as the proximity of the aerofoil in the wall-normal direction is varied.Graphic abstract

Subgrid-scale model for large-eddy simulation of transition and turbulence in compressible flows

This article focuses on a subgrid-scale (SGS) eddy viscosity model based on helicity which is derived from our previous research [Yu et al., “Subgrid-scale eddy viscosity model for helical turbulence,” Phys. Fluids 25, 095101 (2013)] for large-eddy simulation of transition and turbulence in compressible flows. Based on the character of the compressible boundary layer over a flat plate, we obtain from theoretical analysis that this model can automatically distinguish laminar flow and turbulence and can also simulate turbulence well. Meanwhile, an a priori test using direct numerical simulation (DNS) data of a spatially developing flat-plate boundary layer at Ma = 2.25 shows that the helicity model can clearly differentiate laminar, transitional, and turbulent regions. Comparing the numerical simulation results with DNS and other SGS models in the spatially developing boundary-layer over a flat plate, we find that the suggested model could precisely predict the onset of transition, transition peak, skin-friction coefficient, mean velocity profile, mean temperature profile, and turbulence intensities. In the case of a compression ramp, the model can well simulate the bypass-type transition, the separated and reattached points, and the size of the separation bubble in the corner region. Furthermore, the prominent advantage of the proposed model can predict transitional flow exactly with no explicit filtering or dynamic procedure.

A numerical study on viscoelastic boundary layer on flat plate

In this study, the effects of viscoelastic properties of non-Newtonian fluids on the flat plate boundary layer are investigated numerically. The numerical solution is obtained using a second-order parallelized finite volume method based on pressure implicit with splitting of operators’ algorithm. Here, the nonlinear Giesekus model is used as the constitutive equation for numerical simulations. The effects of elasticity number, mobility factor and nonlinear normal stress differences on thickness of boundary layer, displacement thickness, momentum thickness, wall shear stress and drag coefficient are studied in detail. Interestingly, a finite thickness is observed at the leading edge of the flat plate. It is also observed that the boundary layer thickness, surface shear stress and drag coefficient of viscoelastic fluids are less than Newtonian fluids.

Analysis of a drag reduced flat plate turbulent boundary layer via uniform momentum zones

High spatial resolution particle-image velocimetry (PIV) and micro-particle tracking velocimetry (μ-PTV) measurements have been performed to analyze the flow structures in a turbulent flat plate boundary layer undergoing spanwise traveling transversal surface waves. The scope of this investigation is to examine the connection between friction drag reduction and the structural properties of the instantaneous flow fields manipulated by the surface wave. The experiments were conducted for a momentum based Reynolds number of Reθ=2250 at dimensionless wave amplitudes of A+=6, 7, 8, and 11, a wave period of T+=94, and a wave length of λ+=3738. Local drag reduction of up to 4.9% at 0.087 boundary layer thicknesses downstream of the moving surface was measured. The Reynolds shear stress in the logarithmic region (50≤y+≤250) is suppressed due to the surface waves, whereas the wall-normal velocity fluctuations are enhanced in the outer layer. The turbulent contribution term in the Fukagata, Iwamoto, and Kasagi (FIK) friction drag decomposition [18] is reduced by 2.7% due to the dampened Reynolds shear stress above the wave crest. The analysis of the large-scale uniform momentum zones (UMZs) indicates that the population of these zones above the wave trough is nearly identical compared to the non-actuated turbulent boundary layer, while above the wave crest the number of UMZs is decreased by 3.5%. The conditional statistics of the modal velocity based on the near-wall velocity fluctuation evidence that there are strong links between the near-wall flow events and the UMZs. The near-wall flow structures of high fluctuating intensity are less correlated to the large-scale UMZs due to the spanwise surface wave motion, which diminishes the momentum transfer from the outer large-scale energetic structures to the near-wall flow, and thus, leads to the friction drag reduction.

Linear stability analysis on the most unstable frequencies of supersonic flat-plate boundary layers

In current supersonic transition models, the timescale models of the first and second modes are required to reflect the contribution to the transition onset by the development of the unstable modes. However, the existing correlations of the timescales have problems in showing the Mach number effect and temperature effect correctly. In this paper, linear stability analyses are conducted to study the existing correlations of the timescales for the first and second modes, and the Mach number effect and the temperature effect are explicitly involved and discussed in the modeling of the characteristic timescales. It is found that the existing correlation between the timescale of the first mode and the Reynolds number based on the displacement thickness is not suitable for the supersonic situation. The frequency of the most unstable first mode in supersonic cases rises rapidly with the increasing Mach number while the current timescale model fails to predict this tendency, and the step phenomenon appears in the frequency-Reynolds-number curves when the Mach number is high. For the second mode, the Mach number effect on the timescale cannot be reflected entirely in the original correlation. Additionally, the temperature effect is proved to affect the timescales of unstable modes, which is left out by the current model. Considering the Mach number, the wall temperature and the total temperature effects, new correlation models for the characteristic frequency of the first and second mode with the Reynolds number are established, in order to provide guidelines for supersonic transition modeling. Some inconsistencies between the timescale-based transition models and the linear stability theory are also commented in this paper.

The effect of compressibility on the primary global instability of unforced laminar separation bubbles

Laminar separation bubbles present a three-dimensional self-excited instability mechanism which leads to the appearance of spanwise-periodic structures. In incompressible flow, this mechanism was found to become active at conditions in which wave-like, two-dimensional perturbations are only convectively unstable. In the absence of continuous external excitation, the three-dimensional instability is expected to dominate the flow dynamics and initiate the laminar-turbulent transition. This work extends previous analyses by incorporating the effect of compressibility at subsonic conditions. Two-dimensional numerical simulations of a flat-plate boundary layer with a prescribed free-stream deceleration and acceleration are carried out to obtain a set of model laminar separation bubbles. A linear stability analysis is applied then, to study the influence of Reynolds and Mach numbers on the three-dimensional instability.

The experimental study of the weak shock wave action on the boundary layer of the sweep flat plate

The weak shock waves impact on the flow in the boundary layer of the sweep flat plate at Mach number 2 is studied experimentally. The model was installed at a zero angle of attack. Shock waves in the oncoming flow were generated by a two-dimensional roughness on the side wall of the wind tunnel test section. The data were obtained with a two-dimensional roughness on the wall of the wind tunnel and with a smooth wall at sweep angles (35 and 40 degrees) of the leading edge of the flat blunt plate. The measurements were carried out with a constant temperature anemometer.

Criteria of computational grid generation for turbulence models taking into account laminar-turbulent transition

Criteria of structured and unstructured mesh generation for turbulence models taking into account laminar-turbulent transition were developed using flat plate boundary layer flow. It is shown the first near wall cell should be placed in the viscous sublayer in the transition region and stretching factor should not exceed 1.4. For the unstructured meshes all the boundary layer should be covered by prismatic layers. The results of the prediction of the flow around a NLF(1)-0414F airfoil show that the use of relatively coarse meshes provide acceptable accuracy of the solution.

Modelling of the boundary layer disturbances by localized effect of the round membrane

The spatial development of the flat plate boundary layer disturbances by the hot-wire anemometry is experimentally investigated. Controlled disturbances were introduced into the laminar flow by means of a round membrane located on the surface of the model. The impulse motion of a round membrane leads to the formation of longitudinal localized structures and wave packets in the boundary layer. Wave packets consist of a set of straight and oblique waves, differing in their propagation characteristics. The development of wave packets downstream is consistent with the linear theory of hydrodynamic stability.

Modification to Improved Delayed Detached-Eddy Simulation Regarding the Log-Layer Mismatch

The wall-modeled large-eddy simulation branch of the widely used improved delayed detached-eddy simulation (IDDES) method is supposed to resolve the problems of log-layer mismatch and underprediction of skin friction, as claimed by the authors of the IDDES (Shur, M. L., Spalart, P. R., Strelets, M. K., and Travin, A. K., "A Hybrid RANS-LES Model with Delayed DES and Wall-Modeled LES Capabilities," International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 1638–1649). But, some researchers did meet these problems when using the IDDES. Aiming at finding out the reason and seeking a remedy, an analysis of the IDDES is carried out that focuses on the relation between the wall-parallel grid size and the length scale of the energetic turbulent structures at the Reynolds-averaged Navier–Stokes (RANS)/large-eddy simulation (LES) interface, and it reveals that the flaw of the IDDES arises from the fact that, in the IDDES approach, the energetic, large-scale, and stress-carrying turbulent structures in the vicinity of the RANS/LES interface are essentially impossible to well resolve by the LES mode. On the basis of the analysis, a modification to the IDDES is proposed by moving the RANS/LES interface further away from the wall so that, at the RANS/LES interface, the wall-parallel grid size is sufficient to resolve the turbulent structures. The modification is simple in form but has clear physical meaning. Through a series of sensitivity tests, it can be concluded that the modified IDDES does resolve the problems of log-layer mismatch and underprediction of skin friction, and it is applicable to low-, moderate-, and high-Reynolds-number flat plate boundary-layer flows without exception.