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This paper develops a spatial input-output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. This method uses one-way spatial integration to reformulate the problem in terms of spatial evolution equations. The technique is used to examine the effect of localized periodic actuation at a given temporal frequency, based on an experimental set-up in which an active large-scale 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. 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., 34 pages, 12 figures, preliminary work presented in AIAA Aviation 2021 with paper no. 2021-2873

Experiments were performed using an active flow control approach that has shown the ability to significantly reduce the viscous drag in turbulent boundary layers. The purpose of this work was to document the changes in the turbulence characteristics of the boundary layer with the drag reduction. The flow control involved generating a steady spanwise velocity component of the order of vortical structures, indicate a suppression of coherent features in the wall layer. These results are consistent with an underlying mechanism for drag reduction that comes from a suppression of the turbulence producing events in the wall layer associated with the wall streak structure.

A 50 year journey through flow control strategies that seek to achieve viscous drag reduction in turbulent boundary layers is presented. These are shown to focus on different mechanisms underlying ...

Forcing by spanwise opposing jets centered around ${y}^{+}=30$ produces drag reduction of more than 10% at Re${}_{\ensuremath{\tau}}$=550.

The noise of flow over tandem cylinders at $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathit{Re}}_D= 22\, 000$ and its reduction using single dielectric barrier discharge (SDBD) plasma actuators are simulated numerically both to confirm and extend experimental results. The numerical approach is based on large-eddy simulation (LES) for the turbulent flow field, a semi-empirical plasma actuation model, and Lighthill’s theory for acoustic calculation. Excellent agreement between LES and experimental results is obtained for both the baseline flow and flow with plasma control in terms of wake velocity profiles, turbulence intensity, and frequency spectra of pressure fluctuations on the downstream cylinder. The validated flow-field results allow an accurate acoustic analysis based on Lighthill’s equation, which is solved using a boundary-element method. The effectiveness of plasma actuators for reducing noise is clearly demonstrated. In the baseline flow, the acoustic field is dominated by the interaction between the downstream cylinder and the upstream wake. Through suppression of vortex shedding from the upstream cylinder, the interaction noise is reduced drastically by the plasma flow control, and the vortex-shedding noise from the downstream cylinder becomes equally important. At a free-stream Mach number of 0.2, the peak sound pressure level is reduced by approximately 16 dB. This suggests the viability of plasma actuation for active aeroacoustic control of airframe noise.

The coherent structure in the near-field of an axisymmetric turbulent jet at a Reynolds number of 3.8 × 105 and Mach number of 0.3 is experimentally characterized by a vector implementation of the proper orthogonal decomposition (POD). The POD eigenfunctions and associated eigenvalues are extracted at several selected streamwise locations in the initial region. The focus on the near-field is motivated by its importance in numerous technical applications. Results show a rapid energy convergence with POD mode number. Examination of the relative energy contained in the combined azimuthal and radial components of the POD modes reveals that it is comparable to that in the streamwise component. The streamwise evolution of the eigenvalue spectra is characterized by a remarkable variation in the azimuthal mode number energy distribution, leading to the dominance of azimuthal mode m = 1 beyond the end of the jet core. In contrast, a scalar implementation using only the streamwise component shows the dominance of mode m = 2 which is consistent with previous scalar implementations of the POD. For a given azimuthal mode number, the eigenvalue spectra exhibit a broad peak which occurs at a constant value of Strouhal number based on local shear layer momentum thickness and local jet maximum velocity. The phase information required for a local reconstruction of the jet structure is obtained by projecting the POD eigenmodes onto instantaneous realizations of the flow at fixed streamwise locations. The instantaneous realizations are obtained by utilizing cross-stream arrays of multi-sensor probes in conjunction with linear stochastic estimation (LSE). Results clearly show the local dynamic behaviour of each component of the jet structure.

This is a continuation of our work on the use of single dielectric barrier plasma actuators for controlling flow separation on turbine blades in the low-pressure turbine stage at low Reynolds numbers typical of high-altitude cruise. This used a linear cascade of Pratt & Whitney "PakB" shaped blades to provide generic low-pressure turbine conditions. The flow over one of the blades was documented through surface pressure, laser-Doppler velocimetry, and hot-wire measurements. These were used to define the location and size of the separated flow region on the suction side of the blade. Both steady and unsteady plasma actuators were implemented and found to be effective in separation control. For the unsteady actuators, there was an optimum excitation frequency to reattach the flow that corresponded to a Strouhal number, based on the length of the separated zone and the local freestream velocity, equal to unity. The unsteady actuator was more effective than the steady actuator in reattaching the flow while also requiring less power. It was suggested by the experimental results that the mechanism for the steady actuators was turbulence tripping, whereas the mechanism for the unsteady actuators was to generate a train of spanwise structures that promoted mixing.

A transport equation for the intermittency factor is employed to predict the transitional flows in low-pressure turbines. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, μt, with the intermittency factor, γ. Turbulent quantities are predicted by using Menter’s two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model which can produce both the experimentally observed streamwise variation of intermittency and a realistic profile in the cross stream direction. The model had been previously validated against low-pressure turbine experiments with success. In this paper, the model is applied to predictions of three sets of recent low-pressure turbine experiments on the Pack B blade to further validate its predicting capabilities under various flow conditions. Comparisons of computational results with experimental data are provided. Overall, good agreement between the experimental data and computational results is obtained. The new model has been shown to have the capability of accurately predicting transitional flows under a wide range of low-pressure turbine conditions.

This work involves the documentation and control of flow separation that occurs over turbine blades in the low-pressure-turbine (LPT) stage at the low Reynolds numbers typical of high-altitude cruise. We utilize a specially constructed linear cascade that is designed to study the flowfield over a generic LPT cascade consisting of Pratt and Whitney Pak B shaped blades. The center blade in the cascade is instrumented to measure the surface-pressure coefficient distribution. Optical access allows laser-Doppler-velocimetry measurements for boundary-layer profiles. Experimental conditions were chosen to give a range of chord Reynolds numbers from 10 4 to 10 5 , and a range of freestream turbulence levels from u'/U∞ = 0.08 to 2.85%. The surface-pressure measurements were used to define a region of separation and reattachment that depends on the freestream conditions

Turbulent kinetic energy (TKE) budget measurements were conducted for a symmetric turbulent planar wake flow subjected to constant zero, favorable, and adverse pressure gradients. The purpose of this study is to clarify the flow physics issues underlying the demonstrated influence of pressure gradient on wake development, and provide experimental support for turbulence modeling. To ensure the reliability of these notoriously difficult measurements, the experimental procedure was carefully designed on the basis of an uncertainty analysis. Three different approaches were applied for the estimate of the dissipation term. An approach for the determination of the pressure diffusion term together with correction of the bias error associated with the dissipation estimate is proposed and validated with the DNS results of Moser et al (J Fluid Mech (1998) 367:255–289). This paper presents the results of the turbulent kinetic energy budget measurement and discusses their implications for the development of strained turbulent wakes.

This paper examines and contrasts the response of planar turbulent wakes with initially symmetric and asymmetric mean velocity profiles to identical imposed streamwise pressure gradients. The focus on near wake behavior, profile asymmetry, and pressure gradient is motivated by their relevance to high-lift systems for commercial transport aircraft. In the experiments, the symmetric wake is generated by a flat plate with a tapered trailing edge. Active and passive flow control are applied on an identical second plate in order to generate the asymmetric wake. Both favorable and adverse constant pressure gradients are imposed on the wakes by means of a downstream diffuser section with fully adjustable top and bottom wall contour. For both symmetric and asymmetric wakes, the effect of pressure gradient on wake spreading, mean velocity defect decay, and the streamwise evolution of the turbulent stresses are documented in detail. In this manner, the role of asymmetry in strained wake development is isolated. We also gauge the ability of commonly used one- and two-equation turbulence models to predict the streamwise wake evolution observed in the experiments.

A robust method to detect the mean turbulent reattachment location with a flush surface-mounted array of hot-film sensors is presented. The method has the advantages of requiring no sensor calibration, no dependence on the presence of a dominant frequency or oscillation period and it requires no qualitative interpretation of sensor time-series signals. The method is developed by investigating the flow downstream of a backward-facing step. Through computation of the “time of flight” of convected flow disturbances over adjacent sensor pairs, the method offers a quantitative resolution of the mean location of reattachment for turbulent flows.

This paper describes an experimental investigation into the development of a planar turbulent wake under constant adverse and favorable pressure gradient conditions. The focus of the study is on the near-wake due to its relevance to high-lift systems for commercial transport aircraft. The wake is generated by a flat splitter plate with tapered trailing edge. The pressure gradients are imposed as the wake passes through a wind tunnel diffuser test section with fully adjustable top and bottom wall contours. The streamwise pressure gradients imposed on the wake flow field are held constant in each case. The wake initial conditions are maintained identical upstream of the location where the pressure gradient is first imposed. The use of constant pressure gradients, coupled with identical initial conditions, facilitates isolation of the effect of streamwise pressure gradients on the near-field evolution of the wake and provides a clean test case for computational models. In this paper we focus on characterizing the mean flow widening, streamwise velocity defect variation, and the streamwise evolution of turbulence statistics for both favorable and adverse streamwise pressure gradients. The imposed pressure gradients are shown to have a very significant effect on both the mean and turbulent flow quantities.

The topology of the large-scale structure in the similarity region of a turbulent planar jet is investigated experimentally. The large-scale structure is reconstructed in physical space by projection of measured proper orthogonal decomposition eigenmodes onto instantaneous flow-field realizations. The instantaneous flow-field realizations are obtained by a spanwise aligned triple X-wire rake arrangement which is used in conjunction with the linear stochastic estimation technique. Instantaneous realizations are also acquired via a second triple rake arrangement which provides an assessment of the effect of spatial aliasing on the resulting structural topology. Results indicate that the self-similar large-scale structure in the planar jet consists of a dominant planar component consisting of two lines of large-scale spanwise vortices arranged approximately asymmetrically with respect to the jet centreline. This planar component of the structure resembles the classic Karman vortex street. There is a strong interaction between structures on opposite sides of the jet in the form of nearly two-dimensional lateral streaming motions that extend well across the flow. In addition, results indicate that the effect of the nonplanar spanwise modes is to both tilt and bend the primary spanwise vortex tubes and thereby redistribute large-scale vorticity. The bending occurs primarily in the streamwise direction. The degree to which the spanwise vortices are distorted varies greatly; in some cases they are nearly streamwise oriented and in others only slight distortion of a spanwise vortex is noted. Based upon the experimental results, prospects for low-order modelling of the jet large-scale structure are discussed.

An experimental investigation of the nonlinear spectral dynamics involved in the transition of an initially laminar planar jet shear layer at moderate Reynolds number is presented. Application of a two‐point measurement technique allows the quadratic nonlinear transfer function characterizing the local spectral dynamics to be estimated from digitized time‐series fluctuation data. This approach provides a measure of the efficiency of local nonlinear processes and allows the relevant local quadratic wave interactions characterizing the jet shear layer transition to be unambiguously detected and quantified. The results indicate that the jet shear layer shows a strong preference for difference mode interactions. These function initially to produce low frequency modes near the jet column frequency. The finite amplitude saturation of the fundamental is dominated by sum interactions which enrich the harmonic content of the spectrum. The subharmonic resonant interaction is found to be a weakly nonlinear phenomenon that involves a linear growth rate modification of the subharmonic due to its phase couple with the fundamental. Measurements indicate that the phase couple between the subharmonic and fundamental instabilities develops very near the nozzle lip. This resonant interaction between fundamental and subharmonic is found to dominate the global nonlinearity of the shear layer though it is overshadowed locally by stronger sum and difference wave interactions. Evidence is also presented which demonstrates resonant phase coupling between the disturbance sensitive region near the nozzle lip and vortex interaction events in the downstream flow, thereby indicating that a resonant feedback coupling exists between these two regions of the flow field.

The result of an experimental investigation into the natural near‐field transition of an untuned planar jet at moderate Reynolds number is presented. Here the term ‘‘untuned’’ refers to the case where the ratio of the thin shear layer instability frequency to the jet column frequency is not given by an integer power of 2, so that a sequence of shear layer vortex pairing or amalgamation events is incapable of yielding the jet column frequency near the end of the potential core. This case is of interest because the jet shear layer instability must undergo more dramatic frequency and phase adjustments in order to satisfy the downstream jet column constraint. This provides a unique opportunity to investigate how instabilities that scale with the jet column interact with those that scale with the nascent shear layer instability to configure the initial evolution of the natural planar jet. Auto‐bicoherence spectra are used in conjunction with conventional power spectra in order to provide quantitative measurements of the nonlinear phase coupling between wave triads that characterizes the near‐field transition of the natural planar jet. These measurements are complemented by two‐point correlation, coherence, and phase spectra that document the streamwise evolution and cross‐stream symmetry of structural patterns in the flow throughout the initial, interaction, and early self‐preserving regions. These measurements indicate that the wave interactions that characterize the planar jet near‐field transition are quite different from the sequence of subharmonic instabilities that typically characterize the planar mixing layer. In particular, suppression of the subharmonic instability and the formation of modulating sidebands are observed. The modulation occurs at the jet column frequency and the measurements suggest that this has an origin that is due to a kinematic effect associated with the lateral oscillation of the nascent shear layers near the nozzle lip. The origin of this oscillation appears fully consistent with Biot–Savart induction from the downstream region of the flow associated with the loss of symmetry of the large‐scale vorticity field.

An experimental investigation of turbulent boundary layer relaminarization is underway at the Hessert Center for Aerospace Research at the University of Notre Dame. A turbulent boundary layer was exposed to a large favorable pressure gradient for several values of Launder's relaminarization parameter. It was observed that many of the turbulent boundary layer parameters behaved as if the boundary layer relaminarized, despite values of the relaminarization parameter below which relaminarization would be expected. Preliminary results lead one to question the validity of the relaminarization parameter as the proper criterion for the onset of relaminarization. Further, evidence suggests the turbulent burst-sweep event may be a direct indicator of relaminarization and preliminary experimental data supports this claim.

Shock wave/turbulent boundary layer interactions have been the topic of numerous investigations and yet many aspects of the physical mechanisms associated with the interaction remain poorly understood. The extension of low speed turbulence closure models to the interaction region between a shock wave and turbulent boundary layer can lead to predictions of wall pressure distribution, skin friction, mean velocity profile, and turbulence quantities which are far from satisfactoryl. The failure of equilibrium based turbulence models is generally attributed to the extreme rapid distortion of the flow field. Nonequilibrium turbulence closure models based upon rapid distortion theory have met with some success. Anyiwo and Bushnell2 noted, however, that the physics of the turbulent stress amplification which has been experimentally demonstrated to occur across the shock needs to be incorporated into the current generation of rapid distortion theories. A simple linearized model by Anyiwo and Bushnell2 theoretically demonstrates three primary modes of turbulence amplification across the shock: (1) a “direct” inviscid vorticity amplification, (2) conversion of incident acoustic and entropy modes into vortical modes and (3) turbulence production due to shock wave oscillation.

A canonical flat-plate turbulent boundary layer with Re θ = 4590 is exposed to a favourable mean streamwise pressure gradient sufficient to cause relaminarization. The favourable pressure gradient is generated by a linear contraction, yielding a peak value of the acceleration parameter of K = 4.4 × 10 −6 which is sustained for approximately 13 local boundary layer thicknesses. The relaminarization process is characterized by an extensive series of mean flow and turbulence measurements obtained at several representative streamwise locations. In anticipation of the loss of standard log-law behaviour, the local wall shear stress is directly measured using the oil-film interferometry technique. Mean flow measurements show a systematic variation in the Karman and additive constants with applied streamwise strain rate. The series of measurements also indicate an apparent decoupling of the outer and near-wall regions of the accelerating boundary layer. In accord with this, conditional measurements show that fourth-quadrant sweep events are virtually eliminated, while much less frequent but larger-amplitude near-wall second-quadrant ejection events remain. The reduction in fourth-quadrant sweep events is matched by an observed increase in near-wall third-quadrant events. The consequent reduction in near-wall Reynolds stress correlation and associated cross-stream momentum transport results in a large reduction in c f for the relaminarized flow.

The primary objective of this research is to enhance our understanding of the flow field physics associated with shock wave turbulent boundary layer interactions and thereby enable more accurate predictive models to be developed. It is widely recognized that shock wave turbulent boundary layer interactions are very important in a variety of high speed aerodynamic applications and yet, despite much attention to this topic in the past, the dynamic mechanisms involved remain poorly understood. The compression ramp generated shock wave turbulent boundary layer interaction is experimentally investigated in this study. It is a primary objective of this research to isolate the mechanism(s) responsible for the amplification of turbulent stresses through the shock. The interplay between the combined effects of bulk compression, concave curvature, 'direct' amplification and pressure gradient will be clarified. In addition, the dynamic mechanism(s) responsible for shock wave oscillation and the role this oscillation plays in the turbulent stress amplification through the shock will also be examined. Measurements documenting the mechanism of turbulent stress relaxation downstream of shock are also obtained.

An experimental study was performed to determine the effects a periodic acoustic disturbance had upon a two-dimensional turbulent jet in both the initial and similarity regions. Correlation and energy spectra measurements in the initial region indicate that acoustic forcing within a certain frequency range is capable of restructuring the flow in this region. In particular, these measurements suggest the presence of vortical flow structures arranged symmetrically with respect to the jet centerline. Measurements of the mean and turbulent flow structure in the similarity region of the jet indicate strong acoustically induced effects. Evidence suggests that the interaction effects observed in the similarity region are intimately related to those in the initial region.

An experimental investigation into the transition of an initially laminar planar jet at moderate Reynolds number is presented. Very low level acoustic excitation is applied upstream of the nozzle exit in order to organize the initial instability wave and thereby facilitate investigation of its downstream evolution. Particular attention is focused upon quantifying the quadratic nonlinear wave interactions that characterize the near‐field transition as evidenced by measurements of phase locking between resonant wave triads. The spectral evolution of fluctuations in the planar jet shear layer indicate that the subharmonic is significantly suppressed. This subharmonic suppression was found to result from an interesting combination of the dynamics of subharmonic resonance and the upstream feedback of perturbations from the interaction region beyond the jet potential core to the disturbance sensitive region near the nozzle lip. The upstream feedback was found to be associated with the large‐scale restructuring of the flow that characterizes the interaction region of the planar jet and results in the loss of symmetry of the coherent vorticity field with respect to the centerline. The imposed near‐exit perturbations interact nonlinearly with the shear layer instability wave to produce the observed suppression. The interplay between the initial and interaction regions of the flow provides a unique glimpse of the rich behavior that even seemingly simple flows can exhibit during transition to turbulence.

The enhancement of widening rate and turbulence intensity in a turbulent plane jet, due to an acoustic disturbance are considered. Detailed data at a representative Strouhal number suggest a well organized symmetric structural array in the initial region of the flow. These highly organized flow structures act as efficient agents in the transport of energy to the fine-grained turbulence, leading to greater diffusivity, enhanced turbulence and an increase in widening. The data also suggest significant differences in the underlying structure of the natural and excited jet flows, hence putting in jeopardy any generalization of coherent motions especially excited to facilitate their study.

An experimental study of the developing structural characteristics of a two-dimensional jet in an extremely quiet environment was performed. The jet, at an exit Reynolds number of 6000 and with fluctuation intensity under 0.2% at the mouth, was operated within a large anechoic room. Measurements of energy spectra, fluctuation phase angles and two-dimensionality led to the inference of structural patterns in the flow. These patterns are initially characterized by relatively strong symmetric modes exhibiting limited two-dimensionality and oriented parallel to the mouth of the jet. Subsequent downstream evolution led to the formation of an antisymmetric pattern beyond the jet potential core and the associated development of extended structures possessing a definite large lateral inclination. The results of this work suggest a developing large-scale structural pattern more complicated than previously supposed.

An experimental investigation of a developing planar turbulent jet discharging into a quiescent environment was undertaken. The measurements now reported suggest that the pressure field associated with the large‐scale flow structures occurring downstream excite the nascent jet shear layers near the jet exit. Such structures are characterized by the formation of an antisymmetric structural array near the end of the potential core and extending far into the similarity region. The results suggest that coupling or feedback between downstream coherent structures and the initial region may be important in the development of the flow.

An experimental investigation of large‐scale structural patterns in the similarity region of a two‐dimensional turbulent jet was performed. Two‐point correlation and coherence‐based measurements obtained from both longitudinal and lateral component velocity fluctuations are, in general, supportive of the existence of an antisymmetric array of counterrotating vortices in the similarity region. Particularly graphic evidence is obtained from detailed isocorrelation contour maps that are presented. A novel method of determining structural convective velocity is developed and indicates the structural array propagates at 60% of the local centerline mean velocity. Very limited structural two dimensionality is exhibited in the direction of mean flow homogeneity and it is suggested that this is likely to be related to the existence of multiple coherent modes in the flow.