Abstract: This paper describes an experiment in which a forced shear layer external to a turbulent boundary layer is used to impart external large-scale forcing to the boundary layer. The shear-layer forcing creates periodic coherent vortical structures in the shear layer that convect at the shear-layer convective velocity. The convecting coherent structures create a concomitant unsteady pressure field that provides a disturbance for the turbulent boundary layer on the upper wall of the tunnel above the forced shear layer. The unsteady pressure field in turn creates a variation of the effective freestream velocity experienced by the boundary layer, and both the pressure disturbance and the concomitant velocity fluctuations are reported. The character of the turbulence in the boundary layer due to the external forcing is studied through hot-wire anemometry. Thorough examination of the turbulence results in similarities between the turbulence amplitude modulation results due to these externally-forced experiments and modulation response of an internally-forced boundary layer done by others.

ID: CaltechAUTHORS:20160212-132731202

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Abstract: Vertical axis wind turbine (VAWT) blades undergo dynamic separation due to the large angle of attack variation they experience during a turbine rotation. The flow over a single blade was modeled using a sinusoidally pitching and surging airfoil in a constant free stream flow at a mean chord Reynolds number of 10^5. Two-dimensional, time resolved velocity fields were acquired using particle image velocimetry (PIV). Vorticity contours were used to visualize shear layer and vortex activity. A low order model of dynamic separation was developed using Dynamic Mode Decomposition (DMD). A primary and secondary dynamic separation mode were identified as the critical drivers for the unsteady flow field.

ID: CaltechAUTHORS:20150210-091011617

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Abstract: A synthetic spanwise-constant spatio-temporal mode is excited in a flat plate turbulent boundary layer through a spatially impulsive patch of dynamic wall-roughness. The streamwise wavelength of the synthetic mode approximately corresponds to the very large-scale motions present in high Reynolds number wall turbulence. Hot wire anemometer measurements made downstream of the roughness forcing reveal the nature of the two dimensional synthetic large-scale and its influence on the small-scale turbulence. A clear phase organizing effect on the small-scales is noticed in presence of the synthetic large-scale. A thorough understanding of these phase relations lays the foundation for a framework that allows for practical manipulation of energetic small-scale turbulence through large-scale inputs by utilizing the inherent non-linear coupling present in the governing Navier-Stokes equations.

ID: CaltechAUTHORS:20140713-153917772

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Abstract: Aero-optic measurements of turbulent boundary layers were performed in wind tunnels at the University of Notre Dame and California Institute of Technology for heated walls at a range of Reynolds numbers. Temporally resolved measurements of wavefronts were collected at a range of Mach numbers between 0.03 and 0.4 and the range of Re_θ between 1,700 and 20,000. Wavefront spectra for both heated and un-heated walls were extracted and compared to demonstrate that wall heating does not noticeably alter the shape of wavefront spectra in the boundary layer. The effect of Reynolds number on the normalized spectra was also presented, and an empirical spectral model was modified to account for Reynolds number dependence. Measurements of OPD_(rms) for heated walls were shown to be consistent with results from prior experiments, and a method of estimating OPD_(rms) and other boundary layer statistics from wavefront measurements of heated-wall boundary layers was demonstrated and discussed.

ID: CaltechAUTHORS:20141107-115405464

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Abstract: The effects of introducing a two- or three-dimensional streamwise traveling wave type body forcing in a turbulent channel flow at Re_τ = 180 are investigated using direct numerical simulations (DNS). The optimal forcing shape (that is, the forcing that leads to the most amplified or highest-gain velocity response) is obtained from the resolvent analysis of McKeon & Sharma (2010) for wave-numbers and wave-speed representative of the near-wall cycle. The velocity response due to imposed forcing obtained from DNS is found to agree well with resolvent analysis predictions at small forcing amplitude. The changes in mean velocity, shear stress and kinetic energy are characterized for various amplitudes of forcing.

ID: CaltechAUTHORS:20141107-145723375

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Abstract: Despite being one of the earliest - and most studied - active control techniques proposed for wall-bounded turbulent flows, the opposition control method of Choi et al., [J.Fluid Mech., Vol. 262, 1994, pp. 75-110] remains to be fully understood. In this paper, we develop a simple model for opposition control by extending the forcing-response analysis presented in McKeon and Sharma [J. Fluid Mech., Vol. 658, 2010, pp. 336-382]. Based on a gain analysis of the Navier-Stokes equations, the velocity field in turbulent pipe flow is decomposed into a series of highly-amplified response modes (i.e., propagating helical waves). Opposition control, introduced via the boundary condition on wall-normal velocity, alters the amplification characteristics and structure of these response modes, whereby a reduction in gain (mode suppression) leads to a reduction in drag. With simple assumptions, and minimal computation, our model reproduces the leading-order integrated effects of opposition control predicted by DNS. By breaking down opposition control into modal subsystems, our analysis provides new physical insight into the deterioration of control performance with increasing sensor elevation and Reynolds number. We show that opposition control is only effective for specific wavenumber-frequency combinations; others require the introduction of a phase lag between sensed and actuated velocity. Moving forward, this mode-by-mode approach can enable the design and evaluation of targeted control techniques, as well as the definition of a theoretical limit for controller performance.

ID: CaltechAUTHORS:20150211-141351820

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Abstract: The resolvent-based analysis of wall turbulence (McKeon & Sharma 2010) is extended with an explicit treatment of the non-linearity in the Navier-Stokes equations. The equivalent of triadic interaction in the wall-normal direction is described, and it is found that the resulting forcing has a phase shift of π/2 in terms associated with symmetric spatial directions. Explicit forms for the nonlinearity in fully-developed pipe and channel flows, i.e. in cylindrical and Cartesian coordinate systems.

ID: CaltechAUTHORS:20150211-102550604

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Abstract: We evaluate the efficacy of a gain-based rank-1 model, developed by McKeon & Sharma (J. Fluid Mech., 2010), for representing the energy spectra and the streamwise/wall-normal co-spectrum in a turbulent channel. This is motivated by our previous observation that the streamwise turbulent energy intensity is well approximated by the rank-1 model subject to a broadband forcing in the wall-parallel directions and a properly selected temporal intensity. In the present study, the evaluation is based on finding the optimal forcing spectrum that minimizes the deviation between the two-dimensional velocity spectra at different wall-normal locations obtained from direct numerical simulations at friction Reynolds number 2003 (Hoyas & Jiminénez, Phys. Fluids, 2006) and from the rank-1 model at equal Reynolds number. It is shown that the optimally forced rank-1 model captures the streamwise energy spectrum for streamwise wavelengths smaller than approximately 1000 viscous units throughout the channel. For larger wavelengths, the streamwise spectrum is matched in the outer region of the channel, i.e. wall-normal distances larger than approximately 0.15 times the channel half-height, and the mismatch close to the wall results in less than 5 percent error in the inner-scaled peak of the streamwise energy intensity. In addition, we show that the rank-1 model with optimal forcing captures the essential features of the wall-normal and spanwise spectra and the streamwise/wall-normal co-spectrum. We observe that the predicted magnitudes of the latter three spectra are smaller in the rank-1 model compared to the simulation results suggesting that a higher-order or different rank-1 model may be necessary for accurate representation of these spectra.

ID: CaltechAUTHORS:20150218-094025300

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Abstract: Time-resolved DPIV measurements performed in wall parallel planes at several wall normal locations in a turbulent boundary layer (TBL) are used to illuminate the distribution of wall parallel velocities in a three-dimensional energy spectrum over streamwise, spanwise, and temporal wavelengths. To our knowledge, this is the first time this type of spectral distribution has been reported. Slices of the 3D spectrum can give insight into the propagation of different scales in the ow as well as the streamwise and spanwise extent of dominant scales. Measurements were performed at three wall normal locations, y^+ = 34; 108; and 278, in a zero pressure gradient TBL at Re_τ = 470 . Two high speed cameras placed side-by-side in the streamwise direction give a 10δ streamwise field of view with a time step of Δt^+ = 0:5 between consecutive fields. Far from the wall the convection velocities of all scales are very close to the local mean velocity in agreement with the work of Dennis and Nickels, while at y^+ = 34 it was found that all measured scales in the flow convect faster than the local mean in agreement with Krogstad et. al. The variation of the convection velocity with scale and distance from the wall will be discussed.

ID: CaltechAUTHORS:20150226-100222113

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Abstract: Statistical and spectral analyses of the manipulation of a canonical zero pressure gradient turbulent boundary layer using static roughness and low-frequency dynamic roughness patches are presented. A shift of spectral energy away from the wall downstream of the roughness patch is observed. The dynamic roughness is shown to disrupt the structure of the boundary layer, while embedding its periodic signature in an extensive stretch of the downstream flow field.

ID: CaltechAUTHORS:20150226-094906075

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Abstract: An experimental study was undertaken to determine the effects of step excrescences on boundary layer transition using a unique ground test facility in which the test model was propelled though still air. The models used were designed to have a nominally constant pressure gradient so that the results would be relevant to laminar flow aircraft whose wings often have long runs of mildly favorable pressure gradient. The models had an integrated continuously adjustable two-dimensional step, which could be adjusted to be forward-facing or aft-facing. The large model was used to increase the Reynolds numbers examined so that the results are applicable to laminar flow flight vehicles. Multiple measurement methods, including Preston tubes, hot wires, accelerometers, a boundary layer traverse, and static pressure taps were used to provide comparison data, and to add to the physical understanding of the results. The propelled-model test approach required that the instrumentation be self-contained and ride along with the model as the carrier vehicle moved down the test track. Due to the relatively short times available for data-taking (approximately 15-30 seconds per run), the initialization and data analysis techniques had to be tailored for this application.

ID: CaltechAUTHORS:20150303-112035324

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Abstract: We describe a method to investigate the mode shapes in turbulent pipe flow at a given wavenumber pair that are most responsive to harmonic forcing in the sense that the they correspond to the largest singular value in a Schmidt decomposition of the linear Navier-Stokes operator using the turbulent mean profile as the base flow. The ideas follow logically from the work of Sharma & McKeon (2009), who considered a similar approach for laminar pipe flow.

ID: CaltechAUTHORS:20150303-105749150

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Abstract: An examination of the effects of surface step excrescences on boundary layer transition was performed, using a unique experimental facility. The objective of the work was to characterize the variation of transition Reynolds numbers with measurable step size and boundary layer parameters, with the specific goal of specifying new tolerance criteria for laminar flow airfoils, alongside a fundamental investigation of boundary layer transition mechanisms. This paper focuses on interpretation of hot-wire measurements, including supporting stability calculations, undertaken as part of the study. The results for both forward and aft-facing steps indicated a substantial stabilizing effect of favorable pressure gradient on excrescence-induced boundary layer transition. These findings suggest that manufacturing tolerances for laminar flow aircraft could be loosened in areas where even mild favorable pressure gradients exist.

ID: CaltechAUTHORS:20150303-111551041

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Abstract: Manufacturing tolerances for laminar flow wings can be significantly tighter than those of conventional aircraft. The tighter tolerances can significantly affect the assessment of the practicality of designing for laminar flow. However, existing data on the effects of excrescences typical of manufacturing process are limited. Further, information on the effects—often beneficial—of pressure gradient present on the laminar flow wings is not generally available. To address these concerns, a series of experiments has been undertaken to examine the effects of surface steps in the presence of pressure gradients. The step geometries were selected to represent those that result from actual aircraft manufacturing processes. The range of pressure gradients correspond to those typical of laminar flow wings. Initial experiments were conducted in a low-speed wind tunnel. Later experiments used a novel propelled-model test facility. The results of these studies show that the allowable sizes of surface excrescences for laminar flow wings may be significantly greater than has conventionally been assumed. This could significantly influence the more widespread use of laminar flow for drag reduction, resulting in more efficient aircraft.

ID: CaltechAUTHORS:20150303-110715680

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Abstract: Though the effect of distributed roughness on flow over a sphere has been examined in detail, there have been few observations as to the effect of an isolated roughness element on the forces induced on a sphere that is in uniform flow. In this experimental study, we examine how the forces are altered due to both a stationary and dynamic three-dimensional roughness element in the Reynolds number range of 5 x 104 to 5 x 105. It is found that even a small change to the geometry of the sphere, by adding a cylindrical roughness element with a width and height of 1% the sphere diameter, dramatically alters the drag and lateral forces over a wide range of Reynolds numbers. Of particular interest is that the mean of the lateral force magnitude can be increased by a factor of about seven, compared with a stationary stud, by moving the isolated roughness at a constant angular velocity about the sphere. These results can be applied to tripping a laminar boundary layer, steering a bluff body, and increasing the mixing of two fluids, using a minimal amount of energy input. This research is a first step towards understanding the interaction between time dependent surface motion and the subsequent alteration of the location of the boundary layer separation line and wake development.

ID: CaltechAUTHORS:20150303-112614795

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Abstract: First experimental measurements of manipulation of the structure of a canonical zero pressure gradient turbulent boundary layer using a low frequency (compared to the viscous frequency) mechanical dynamic roughness are presented. “Dynamic” (or time-dependent) surface roughness is proposed as a method for both control and diagnosis of turbulent boundary layers.

ID: CaltechAUTHORS:20150303-113157017

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Abstract: The response of pipe flow to physically realistic, temporally and spatially continuous(periodic) forcing is investigated by decomposing the resolvent into orthogonal forcing and response pairs ranked according to their contribution to the resolvent 2-norm. Modelling the non-linear terms normally neglected by linearisation as unstructured forcing permits qualitative extrapolation of the resolvent norm results beyond infinitesimally small perturbations to the turbulent case. The concepts arising have a close relationship to input output transfer function analysis methods known in the control systems literature. The body forcings that yield highest disturbance energy gain are identified and ranked by the decomposition and a worst-case bound put on the energy gain integrated across the pipe cross-section. Analysis of the spectral variation of the corresponding response modes reveals interesting comparisons with recent observations of the behavior of the streamwise velocity in high Reynolds number (turbulent) pipe flow, including the importance of very long scales of the order of ten pipe radii, in the extraction of turbulent energy from the mean flow by the action of turbulent shear stress against the velocity gradient.

ID: CaltechAUTHORS:20141107-113657314

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Abstract: Vortex shedding and turbulent motion in the wake of a sphere that is supported using a streamwise-aligned cylindrical sting are investigated at a subcritical Reynolds number of Re=3800, using high speed particle image velocimetry. The mechanism by which the presence of a sting of increasing diameter relative to the diameter of the sphere influences the wake, in terms of both the small-scale shear instability and the larger wake instability, is explored and brie y compared with the two-dimensional analog of the splitter plate introduced into a cylinder wake. The difficulties associated with obtaining converged statistics, along with the effect of free stream turbulence and sphere vibrations are detailed. An understanding of the mechanism by which the blockage, or interference, arising from the presence of the sting influences cross-wake communication and downstream development is a necessary precursor to studies of active control of the wake using surface actuation on a sting-mounted sphere.

ID: CaltechAUTHORS:20150303-113517097

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Abstract: High Reynolds number pipe flow data are used to demonstrate the importance of several conditions related to scale separation that are either assumed in the classical theories or may be used in light of recent results in wall turbulence to infer a minimum Reynolds number condition above which scaling results may be suitable for extrapolation. Results from the Princeton Superpipe have suggested Re_τ > 5000 as the minimum Reynolds number for which key properties of pipe flow reach a “fully-developed” condition, based on observations of streamwise mean and turbulent velocity structure. Additional values related to finer constraints on the structural development are also discussed. A “skeleton” of wall turbulence is introduced, based on structural components identified as having a dominant role in the dynamics of near-wall turbulence in recent experiments by a variety of authors. Possible interaction mechanisms between these components are described alongside some outstanding questions concerning scale separation and interaction.

ID: CaltechAUTHORS:20141107-121005176

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Abstract: An experimental investigation of the transition process in boundary layers subjected to forward- or aft-facing two-dimensional step excrescences is described. The objective of the work was to characterize the variation of transition Reynolds numbers with measurable roughness and boundary layer parameters, with the specific goal of specifying new tolerance criteria for laminar flow airfoils, alongside a fundamental investigation of linear boundary layer stability mechanisms. Results from an ongoing program of increasing complexity on effects of pressure gradient on excrescence-induced transition are presented. Preliminary N-factor calculations are used to determine the effects of boundary layer stability and attempt to isolate the effect of the disturbance due to the excrescence.

ID: CaltechAUTHORS:20150303-121020776

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Abstract: A method for nonlinear global stabilisation of the incompressible Navier-Stokes equations is presented and used to eliminate transient growth in linearly stable Poiseuille flow for the case of full-field actuation and sensing. In the absence of complete velocity field sensing and full actuation the controller synthesis procedure gives a controller that minimises the the attainable perturbation energy over all disturbances and thus maximises the disturbance threshold for transition to occur. The control laws are found using the theory of positive real systems, originating in the control systems community. It is found that a control law making the linearised part of the perturbed Navier-Stokes equations positive real, provides nonlinear global stability. A state-space synthesis procedure is presented that results in two game-theoretic algebraic Riccati equations.

ID: CaltechAUTHORS:20150303-121446831

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Abstract: Statistics of the streamwise velocity component in fully-developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 < Re_D < 5.7 x 10^6. The second moment exhibits two maxima: one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, is also Reynolds-number dependent and follows roughly the peak in Reynolds shear stress. The behaviour of both peaks is consistent with the concept of inactive motion which increases with increasing Reynolds number and decreasing distance from the wall. No simple scaling is apparent, and in particular, so-called "mixed" scaling is no better than wall scaling in the viscous sublayer and is actually worse than wall scaling in the outer region. The second moment is compared with empirical and theoretical scaling laws and some anomalies are apparent. The scaling of spectra using y, R and u_τ is examined. It appears that even at the highest Reynolds number, they exhibit incomplete similarity only: while spectra do collapse with either inner or outer scales for limited ranges of wave number, these ranges do not overlap. Thus similarity may not be described as complete and any apparent k_1^(-1) range does not attract any special significance and does not involve universal constants. It is suggested that this is because of the influence of inactive motion. Spectra also show the presence of very long structures close to the wall.

ID: CaltechAUTHORS:20150304-112212308

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