Sensitivity of high-speed boundary-layer stability to base-flow distortion

2018 ◽  
Vol 859 ◽  
pp. 476-515 ◽  
Author(s):  
J. Park ◽  
T. A. Zaki
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
High Speed ◽  
Phase Speed ◽  
Streamwise Velocity ◽  
Base Flow ◽  
Critical Layer ◽  
Base Temperature ◽  
Flow Distortion ◽  
Lagrangian Optimization

The linear stability of high-speed boundary layers can be altered by distortions to the base velocity and temperature profiles. An analytic expression for the sensitivity is derived for parallel and spatially developing boundary layers, the latter using linear parabolized stability equations and their adjoint. Both the slow mode, S, and the fast mode, F, are investigated at Mach number 4.5. The mode S is more sensitive with respect to distortion in base velocity than in base temperature. The sensitivity is largest within the boundary layer away from the wall. Near the critical layer, where the phase speed of the mode equals the base streamwise velocity, the sensitivity to the base streamwise velocity is negative. For the mode F, there is a discontinuous jump in the sensitivity when the phase speed is below unity, and a critical layer is established. The sensitivity of the two modes increases with the Reynolds number, but there is a sudden drop and a jump in the sensitivities of the modes S and F, respectively, near the synchronization point where the phase speeds of the two modes are equal. Furthermore, the maximum uncertainty bounds are obtained for the distorted base state that maximizes the destabilization or stabilization of the modes by solving the Lagrangian optimization problem for the sensitivity. The sensitivity of the flow stability to surface heating is then studied, and changes in growth rate and the$N$-factor are evaluated. The formulation provides a clear physical interpretation of these changes, and establishes uncertainty bounds for stability predictions for a given level of uncertainty in wall temperature.

Streak instabilities in boundary layers beneath free-stream turbulence

2014 ◽  
Vol 741 ◽  
pp. 280-315 ◽  
Author(s):  
M. J. P. Hack ◽  
T. A. Zaki
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
High Speed ◽  
Free Stream ◽  
Adverse Pressure Gradient ◽  
Base Flow ◽  
Bypass Transition ◽  
Low Speed ◽  
Free Stream Turbulence ◽  
Low Speed Streaks

AbstractThe secondary instability of boundary layer streaks is investigated by means of direct stability analysis. The base flow is computed in direct simulations of bypass transition. The random nature of the free-stream perturbations causes the formation of a spectrum of streaks inside the boundary layer, with breakdown to turbulence initiated by the amplification of localized instabilities of individual streaks. The capability of the instability analysis to predict the instabilities which are observed in the direct numerical simulation is established. Furthermore, the analysis is shown to identify the particular streaks that break down to turbulence farther downstream. Two particular configurations of streaks regularly induce the growth of these localized instabilities: low-speed streaks that are lifted towards the edge of the boundary layer, and the local overlap between high-speed and low-speed streaks inside the boundary layer. It is established that the underlying modes can be ascribed to the general classification of inner and outer modes which was introduced by Vaughan & Zaki (J. Fluid Mech., vol. 681, 2011, pp. 116–153). Statistical evaluations show that Blasius boundary layers favour the amplification of outer instabilities. Adverse pressure gradient promotes breakdown to turbulence via the inner mode.

Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

2018 ◽  
Vol 856 ◽  
pp. 135-168 ◽  
Author(s):  
S. T. Salesky ◽  
W. Anderson
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Small Scale ◽  
Convective Conditions ◽  
Wide Range

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

Boundary Layers and Skin Friction in High-Speed Flow

1951 ◽  
Vol 55 (485) ◽  
pp. 285-302 ◽  
Author(s):  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
High Speed ◽  
Scale Effects ◽  
Practical Interest ◽  
High Speed Flow ◽  
High Speeds ◽  
Speed Flow ◽  
The Subject ◽  
Small Disturbances

SummaryIn this paper an attempt is made to review present knowledge of the subject of boundary layers at high speeds, without delving too deeply into the theory, and to draw attention to the results of practical interest. The introductory remarks describe broadly the special features of boundary layers in compressible flow, namely the existence of both thermal and velocity layers and their interdependence, the sensitivity of the external flow to the layers, and their inter-action with shock waves. The results of importance arising from the theory of the laminar boundary layer and of its stability to small disturbances are then discussed, followed by a summary of the present inadequate state of knowledge of turbulent boundary layer characteristics. It is noted that progress in the latter must await the production of more experimental data. The paper concludes with a discussion of scale effects and the allied problem of boundary layer—shock wave inter-action.

Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate

1996 ◽  
Vol 326 ◽  
pp. 1-36 ◽  
Author(s):  
FréDÉRic Ducros, Pierre Comte ◽  
Marcel Lesieur
Keyword(s):  
Boundary Layer ◽  
Structure Function ◽  
Flat Plate ◽  
High Speed ◽  
Large Scale ◽  
Phase Speed ◽  
Transition To Turbulence ◽  
Order Structure ◽  
Spanwise Direction ◽  
Large Eddy

It is well known that subgrid models such as Smagorinsky's cannot be used for the spatially growing simulation of the transition to turbulence of flat-plate boundary layers, unless large-amplitude perturbations are introduced at the upstream boundary: they are over-dissipative, and the flow simulated remains laminar. This is also the case for the structure-function model (SF) of Métais & Lesieur (1992). In the present paper we present a sequel to this model, the filtered-structure-function (FSF) model. It consists of removing the large-scale fluctuations of the field before computing its second-order structure function. Analytical arguments confirm the superiority of the FSF model over the SF model for large-eddy simulations of weakly unstable transitional flows. The FSF model is therefore used for the simulation of a quasi-incompressible (M∞ = 0.5) boundary layer developing spatially over an adiabatic flat plate, with a low level of upstream forcing. With the minimal resolution 650 × 32 × 20 grid points covering a range of streamwise Reynolds numbers Rex1 ε [3.4 × 105, 1.1 × 106], transition is obtained for 80 hours of time-processing on a CRAY 2 (whereas DNS of the whole transition takes about ten times longer). Statistics of the LES are found to be in acceptable agreement with experiments and empirical laws, in the laminar, transitional and turbulent parts of the domain. The dynamics of low-pressure and high-vorticity distributions is examined during transition, with particular emphasis on the neighbourhood of the critical layer (defined here as the height of the fluid travelling at a speed equal to the phase speed of the incoming Tollmien–Schlichting waves). Evidence is given that a subharmonic-type secondary instability grows, followed by a purely spanwise (i.e. time-independent) mode which yields peak-and-valley splitting and transition to turbulence. In the turbulent region, flow visualizations and local instantaneous profiles are provided. They confirm the presence of low- and high-speed streaks at the wall, weak hairpins stretched by the flow and bursting events. It is found that most of the vorticity is produced in the spanwise direction, at the wall, below the high-speed streaks. Isosurfaces of eddy viscosity confirm that the FSF model does not perturb transition much, and acts mostly in the vicinity of the hairpins.

scholarly journals Reattachment streaks in hypersonic compression ramp flow: an input–output analysis

2019 ◽  
Vol 880 ◽  
pp. 113-135 ◽  
Author(s):  
Anubhav Dwivedi ◽  
G. S. Sidharth ◽  
Joseph W. Nichols ◽  
Graham V. Candler ◽  
Mihailo R. Jovanović
Keyword(s):  
Boundary Layer ◽  
Streamwise Velocity ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Streamwise Vorticity ◽  
Input Output ◽  
Output Analysis ◽  
Input Output Analysis ◽  
Boundary Layer Interaction ◽  
Compression Ramp

We employ global input–output analysis to quantify amplification of exogenous disturbances in compressible boundary layer flows. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks in a hypersonic flow over a compression ramp. Our analysis of the laminar shock–boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat-flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favourably with observations from two different hypersonic compression ramp experiments. Furthermore, our analysis of inviscid transport equations demonstrates that base-flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Finally, the appearance of the temperature streaks near reattachment is triggered by the growth of streamwise velocity and streamwise vorticity perturbations as well as by the amplification of upstream temperature perturbations by the reattachment shock.

A ‘turbulent spot’ in an axisymmetric free shear layer. Part 1

1980 ◽  
Vol 98 (1) ◽  
pp. 65-95 ◽  
Author(s):  
M. Sokolov ◽  
A. K. M. F. Hussain ◽  
S. J. Kleis ◽  
Z. D. Husain
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
Large Scale ◽  
Mixing Layer ◽  
Streamwise Velocity ◽  
Reynolds Stresses ◽  
Free Shear Layer ◽  
Turbulent Spot ◽  
Air Jet ◽  
Phase Average

A three-dimensional ‘turbulent spot’ has been induced in the axisymmetric free mixing layer of a 12.7 cm diameter air jet by a spark generated at the nozzle boundary layer upstream of the exit. The spot coherent-structure signature, buried in the large-amplitude random fluctuating signal, has been educed at three downstream stations within the apparent self-preserving region of the mixing layer (i.e. x/D = 1.5, 3.0 and 4.5) at the jet exit speed of 20 ms−1. The eduction has been performed through digital phase averaging of the spot signature from 200 realizations. In order to reduce the effect of the turbulence-induced jitter on the phase average, individual filtered signal arrays were optimally time-aligned through an iterative process of cross-correlation of each realization with the ensemble average. Further signal enhancement was achieved through rejection of realizations requiring excessive time shifts for alignment. The number of iterations required and the fraction of realizations rejected progressively increase with the downstream distance and the radial position.The mixing-layer spot is a large-scale elongated structure spanning the entire width of the layer but does not appear to exhibit a self-similar shape. The dynamics of the mixing-layer spot and its eduction are more complicated than those of the boundary-layer spot. The spot initially moves downstream essentially at a uniform speed across the mixing layer, but further downstream it accelerates on the high-speed side and decelerates on the low-speed side. This paper discusses the data acquisition and processing techniques and the results based on the streamwise velocity signals. Phase average distributions of vorticity, pseudo-streamlines, coherent and background Reynolds stresses and further dynamics of the spot are presented in part 2 (Hussain, Kleis & Sokolov 1980).

scholarly journals Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011 ◽  
Vol 681 ◽  
pp. 116-153 ◽  
Author(s):  
NICHOLAS J. VAUGHAN ◽  
TAMER A. ZAKI
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Low Frequency ◽  
Finite Amplitude ◽  
Base Flow ◽  
Streamwise Vorticity ◽  
Mean Flow ◽  
S Wave ◽  
Flow Distortion ◽  
Tollmien Schlichting

The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the Tollmien–Schlichting (T–S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

On the generation of steady streamwise streaks in flat-plate boundary layers

2012 ◽  
Vol 698 ◽  
pp. 211-234 ◽  
Author(s):  
Jens H. M. Fransson ◽  
Alessandro Talamelli
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
High Speed ◽  
Control Method ◽  
Plate Boundary ◽  
High Amplitude ◽  
Base Flow ◽  
Stream Velocity ◽  
Bypass Transition ◽  
Streamwise Streaks

AbstractA study on the generation and development of high-amplitude steady streamwise streaks in a flat-plate boundary layer is presented. High-amplitude streamwise streaks are naturally present in many bypass transition scenarios, where they play a fundamental role in the breakdown to turbulence process. On the other hand, recent experiments and numerical simulations have shown that stable laminar streamwise streaks of alternating low and high speed are also capable of stabilizing the growth of Tollmien–Schlichting waves as well as localized disturbances and to delay transition. The larger the streak amplitude is, for a prescribed spanwise periodicity of the streaks, the stronger is the stabilizing mechanism. Previous experiments have shown that streaks of amplitudes up to 12 % of the free stream velocity can be generated by means of cylindrical roughness elements. Here we explore the possibility of generating streaks of much larger amplitude by using a row of miniature vortex generators (MVGs) similar to those used in the past to delay or even prevent boundary layer separation. In particular, we present a boundary layer experiment where streak amplitudes exceeding 30 % have been produced without having any secondary instability acting on them. Furthermore, the associated drag with the streaky base flow is quantified, and it is demonstrated that the streaks can be reinforced by placing a second array of MVGs downstream of the first one. In this way it is possible to make the control more persistent in the downstream direction. It must be pointed out that the use of MVGs opens also the possibility to set up a control method that acts twofold in the sense that both transition and separation are delayed or even prevented.

Evolution of zero-pressure-gradient boundary layers from different tripping conditions

2015 ◽  
Vol 783 ◽  
pp. 379-411 ◽  
Author(s):  
I. Marusic ◽  
K. A. Chauhan ◽  
V. Kulandaivelu ◽  
N. Hutchins
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Initial Conditions ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Mean Flow ◽  
Flow Parameters ◽  
The Mean ◽  
Inflow Conditions

In this paper we study the spatial evolution of zero-pressure-gradient (ZPG) turbulent boundary layers from their origin to a canonical high-Reynolds-number state. A prime motivation is to better understand under what conditions reliable scaling behaviour comparisons can be made between different experimental studies at matched local Reynolds numbers. This is achieved here through detailed streamwise velocity measurements using hot wires in the large University of Melbourne wind tunnel. By keeping the unit Reynolds number constant, the flow conditioning, contraction and trip can be considered unaltered for a given boundary layer’s development and hence its evolution can be studied in isolation from the influence of inflow conditions by moving to different streamwise locations. Careful attention was given to the experimental design in order to make comparisons between flows with three different trips while keeping all other parameters nominally constant, including keeping the measurement sensor size nominally fixed in viscous wall units. The three trips consist of a standard trip and two deliberately ‘over-tripped’ cases, where the initial boundary layers are over-stimulated with additional large-scale energy. Comparisons of the mean flow, normal Reynolds stress, spectra and higher-order turbulence statistics reveal that the effects of the trip are seen to be significant, with the remnants of the ‘over-tripped’ conditions persisting at least until streamwise stations corresponding to $Re_{x}=1.7\times 10^{7}$ and $x=O(2000)$ trip heights are reached (which is specific to the trips used here), at which position the non-canonical boundary layers exhibit a weak memory of their initial conditions at the largest scales $O(10{\it\delta})$, where ${\it\delta}$ is the boundary layer thickness. At closer streamwise stations, no one-to-one correspondence is observed between the local Reynolds numbers ($Re_{{\it\tau}}$, $Re_{{\it\theta}}$ or $Re_{x}$ etc.), and these differences are likely to be the cause of disparities between previous studies where a given Reynolds number is matched but without account of the trip conditions and the actual evolution of the boundary layer. In previous literature such variations have commonly been referred to as low-Reynolds-number effects, while here we show that it is more likely that these differences are due to an evolution effect resulting from the initial conditions set up by the trip and/or the initial inflow conditions. Generally, the mean velocity profiles were found to approach a constant wake parameter ${\it\Pi}$ as the three boundary layers developed along the test section, and agreement of the mean flow parameters was found to coincide with the location where other statistics also converged, including higher-order moments up to tenth order. This result therefore implies that it may be sufficient to document the mean flow parameters alone in order to ascertain whether the ZPG flow, as described by the streamwise velocity statistics, has reached a canonical state, and a computational approach is outlined to do this. The computational scheme is shown to agree well with available experimental data.

scholarly journals Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers

2016 ◽  
Vol 797 ◽  
pp. 683-728 ◽  
Author(s):  
Xuesong Wu ◽  
Ming Dong
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Base Flow ◽  
Bypass Transition ◽  
Leading Order ◽  
Compressible Boundary Layers ◽  
Characteristic Wavelength ◽  
Incompressible Boundary ◽  
Edge Layer

The fundamental difference between continuous modes of the Orr–Sommerfeld/Squire equations and the entrainment of free-stream vortical disturbances (FSVD) into the boundary layer has been investigated in a recent paper (Dong & Wu, J. Fluid Mech., vol. 732, 2013, pp. 616–659). It was shown there that the non-parallel-flow effect plays a leading-order role in the entrainment, and neglecting it at the outset, as is done in the continuous-mode formulation, leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy. The analysis, which was for incompressible boundary layers and for FSVD with a characteristic wavelength of the order of the local boundary-layer thickness, is extended in this paper to compressible boundary layers and FSVD with even shorter wavelengths, which are comparable with the width of the so-called edge layer. Non-parallelism remains a leading-order effect in the present scaling, which turns out to be more general in that the equations and solutions in the previous paper are recovered in the appropriate limit. Appropriate asymptotic solutions in the main and edge layers are obtained to characterize the entrainment. It is found that when the Prandtl number $\mathit{Pr}<1$, free-stream vortical disturbances of relatively low frequency generate very strong temperature fluctuations within the edge layer, leading to formation of thermal streaks. A composite solution, uniformly valid across the entire boundary layer, is constructed, and it can be used in receptivity studies and as inlet conditions for direct numerical simulations of bypass transition. For compressible boundary layers, continuous spectra of the disturbance equations linearized about a parallel base flow exhibit entanglement between vortical and entropy modes, namely, a vortical mode necessarily induces an entropy disturbance in the free stream and vice versa, and this amounts to a further non-physical behaviour. High Reynolds number asymptotic analysis yields the relations between the amplitudes of entangled modes.

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