Robert S. Downs

Transient Growth and Transition Induced by Random Distributed Roughness

Recent experiments on transient disturbances generated by three-dimensional roughness have used spanwise-periodic arrays of geometrically simple cylindrical roughness elements. Connecting these laboratory experiments to more realistic situations requires the study of surfaces with distributed roughness. This is accomplished in this work by numerically generating quasi-random rough surfaces and manufacturing these surfaces using rapid-prototyping technology. Measurements of the disturbances that the rough surface creates in a Blasius boundary layer are obtained for three test configurations corresponding to roughness-based Reynolds numbers of Re k = 164, 227 and 301. The two lower values give laminar flow; the highest value results in localized transition approximately 140 mm downstream of the leading edge of the roughness. All three configurations exhibit transient growth of steady disturbances. Unsteady fluctuations indicate that transition in the Re k =301 configuration is likely an example of a bypass transition mechanism in which the unsteady-disturbance growth outpaces the stabilizing relaxation of the steady flow. Measurements above the roughness surface in the Re k = 227 configuration provide a phenomenological model for distributed receptivity.

Flow Quality Measurements in the Klebanoff-Saric Wind Tunnel

The Klebanoff-Saric Wind Tunnel is a low-speed, closed-return facility with lowdisturbance flow capabilities suitable for boundary-layer stability and transition studies. Previously known as the Arizona State University (ASU) Transition Facility or the ASU Unsteady Wind Tunnel, the tunnel was relocated to Texas A&M University in 2005. During its subsequent reconstruction, several component modifications were introduced, including more advanced acoustic treatments, pneumatic isolation, duct reshaping, and motor-drive alterations, to further enhance flow quality and experimental control. Details regarding the tunnel capabilities, flow quality improvements and tunnel calibration are provided. Freestream turbulence and acoustic measurements are given.

Passive Laminar Flow Control at Low Turbulence Levels

S PANWISE arrays of discrete roughness elements (DREs) are used in wind tunnel and flight experiments to excite stationary crossflow vortices (a recent example is [1]). Because flight turbulence intensities are low, the stationary crossflow mode dominates the traveling mode in that environment and leaves surface roughness as the important initiator of stationary crossflow vortices [2]. A precursor to using arrays of DREs, the experiments by Radeztsky et al. [3] examined the role of isolated roughness elements on steady crossflow mode-packet initiation and growth. Small circular roughness elements (height k of 6 μm and diameter d less than half of the most unstable crossflow mode wavelength) applied near the neutral stability point effectively initiated crossflow vortices in a swept-wing boundary layer. As a result, the average transition location across the span x∕cjtr was advanced upstream by as much as 0.30c. Reibert et al. [4] used arrays of DREs to excite uniform series of stationary crossflow vortices. In addition to nonlinear saturation of the disturbance amplitudes, several important observations regarding theDRE arrayweremade.When the roughness spacing λkwas that of the most unstable or critical crossflow wavelength (λk λcr 12 mm in those experiments), the strong growth of disturbances modulatedwith λcr and λcr∕2was observed. Increasing the roughness spacing to λk 36 mm (3λcr) produced a crossflow disturbance spectrally composed of λk and its first eight harmonics (18–4 mm). No subharmonics were observed in the wavelength spectrum. Saric et al. [5] recognized the importance of the absent subharmonics and used a DRE array with λk 8 mm to excite a stationary crossflow disturbance that was eventually less unstable than the naturally arising λcr disturbance. In doing so, the growth of λcr was suppressed. The remarkable effect of these so-called control DREs in this experiment was to extend laminar flow past the pressure minimum. The potential for passive control of the crossflow instability stimulated a series of wind-tunnel and flight experiments examining this prospect. To extend the results of Saric et al. [5] to higherRec, the flight experiments of Carpenter et al. [6] investigated the effectiveness of DREs in a 30 deg swept-wing boundary layer at Rec 7.5 × 10. Applique DREs and variable-height DREs spaced at λcr (4.5 mm, in this case) were used. Although measurements from a spanwise array of hot-film sensors confirmed that the roughness did excite disturbances of the expected wavelength, x∕cjtr was unchanged below a critical roughness height. Continuing these experiments, Saric et al. [7] delayed the transition using 24-μm-high DREs spaced at λk 2.25 mm (half of the most unstable wavelength) with a painted leading edge; the extent of laminar flow was increased to 0.60c. In recent wind-tunnel experiments, Hunt and Saric [8] demonstrated that the amplitude of disturbances created by the DREs increases linearlywith k. In these experiments, DREs spaced at λcr 12 mm moved the transition forward via stationary crossflow mode growth. However, the expected control using DREs with λk 6 mm was not achieved. Reduced freestream turbulence in the Klebanoff–Saric wind tunnel (KSWT) might be responsible for rendering the control DREs ineffective in these experiments. This possibility prompted Downs [9] to examine the effect of moderate freestream turbulence on crossflow instability using one option for control roughness with λk 6 mm. Although increasing the turbulence intensity Tu was shown to destabilize the boundary layer in the baseline and critical roughness configurations, little change to x∕cjtr was observed with control roughness at Rec 2.8 × 10. The role of higher freestream turbulence was also examined through experimentation by Muller and Bippes [10]. Although control was achieved at the Arizona State University (ASU) unsteady wind tunnel (UWT) by Saric et al. [5], it has proven difficult to realize both in flight (successful control was shown only once by Saric et al. [7]) and at the Texas AM the levels measured in flight and at the KSWT are lower than at the ASU UWT. The objective of this work is to determine if laminar flow control can be achieved through the use of DREs at Tu < 0.04%. To answer this question, the transition locations behind DRE arrays of various wavelengths and heights are measured and compared to baseline roughness cases. These experiments are conducted in the KSWT, which has freestream turbulence intensity (vortical component) of approximately 0.02% [11] (u 0 rms values quoted in [11] are the complete signal; this value is computed using a sound/turbulence separation technique). Previous wind-tunnel experiments in which DRE transition control was effective were conducted in a freestream turbulence intensity of approximately 0.04% [12].

Direct Numerical Simulations of Flow Past Random Distributed Roughness

Nomenclature U∞ = free-stream velocity U, V, W = streamwise, wall-normal, and spanwise velocities F = forcing function used in immersed boundary technique Udes = desired velocity α, β = constants used in immersed boundary technique k = maximum roughness height Rek = roughness based Reynolds number, (U(k)k/ν) Rex = Reynolds number Re’ = unit Reynolds number, U∞/ν ν = kinematic viscosity x, y, z = streamwise, wall-normal, and spanwise coordinates λk = spanwise roughness element spacing (32 mm) δ = boundary layer thickness, (x/Re’) 1/2

Transient Growth due to Surface Roughness: Theory, Simulation and Experiment

Boundary layer receptivity to physically realizable, sub-optimal disturbances has attracted research efforts using theoretical, experimental and numerical tools. Progress requires these approaches be used in a complementary fashion and reach mutual agreement. The present work compares results from each on the sub-optimal transient growth due to surface roughness. New experimental error analyses and comparison to direct numerical simulation (DNS) is shown for three-dimensional discrete roughness elements. Biorthogonal decomposition of DNS results to obtain the continuous spectrum distribution is presented and contrasted with optimal and linear receptivity cases. Realizable disturbances are shown to be sub-optimal and to evolve linearly over large portions of the measurement domain. A technique for performing the decomposition into continuous spectrum modes without pressure and wall-normal velocity measurements is demonstrated and is shown to be effective when the measurable disturbances are of sufcient accuracy.

Disturbances Generated by Random and Periodic Surface Roughness: Experiments and Models

Experiments and simulations that consider how three-dimensional surface roughness affects laminar-to-turbulent transition have a history of mixed success. Two-dimensional roughness has been well understood as a generator of Tollmien‐Schlichting waves. Three-dimensional roughness has been less well understood but is now the subject of increased attention associated with the development of transient growth theory. Experiments that address the receptivity and growth of transient disturbances generated by roughness arrays and models of these processes are reviewed here. Additionally, an extension to random, distributed roughness that takes advantage of manufactured surfaces is described and implemented. The approach lends itself to rigorous comparisons between experimental and simulation data and theoretical models.

Experimental Investigation of the Crossflow Instability in Moderate Freestream Turbulence

The crossflow instability that arises in swept-wing boundary layers is sensitive to freestream turbulence and surface roughness. Although the effects of these disturbance sources comprise a wide body of existing research, there has been little work focusing on low to moderate levels of freestream turbulence (0.02% to 0.2%). Comparison of the results from low-turbulence wind tunnels suggests that freestream turbulence in this range may play a role beyond traveling mode initiation. Development of the stationary crossflow mode in moderate levels of freestream turbulence is measured in the boundary layer of a 45-degree swept wing. Compared with the baseline turbulence level of 0.02%, a reduction in the stationary disturbance amplitudes is observed for turbulence intensities as low as 0.05%. The uncertainties in these measurements are estimated using a Monte Carlo simulation approach.

Using in-Flight Model Yaw Variations to Improve Power Spectrum Estimation of Stationary Crossflow Vortices

In-flight measurement of stationary crossflow vortices on 30-degree swept-wing models is described for two flight testing programs. Excitation of crossflow wavelengths is accomplished using spanwise arrays of Discrete Roughness Elements (DREs). Multielement, surface-mounted hotfilm sensor arrays are used for these measurements. As such measurements are typically limited by the small numbers of anemometer channels available on test aircraft, a novel approach for improving the spectral resolution of these measurements is developed and applied. The nominally stationary crossflow vortices actually meander in the spanwise direction during model yaw variations; removing these spanwise shifts from multiple instants in time produces densely sampled sets of data. A least-squares spectral analysis is applied to this unevenly spaced data to produce well-resolved wavelength spectra. The results of this spectral analysis are discussed in the context of linear stability theory calculations and the effectiveness of DREs at exciting crossflow disturbances is evaluated.

Evaluation of Miniature Vortex Generators for Flow Control in Falkner-Skan Boundary Layers

Vortex generators with heights comparable to displacement thickness are an effective means of producing persistent mean-flow streaks in laminar boundary layers. Inducing streaky base flows can supp ...

Quantifying sub-optimal transient growth using biorthogonal decomposition

Receptivity calculations are shown for physically-realizable, roughnessinduced disturbances. These calculations give the continuous-spectrum amplitude distribution for sub-optimal disturbances for both DNS and experimental data. A technique for computing the amplitude distribution with only streamwise data is shown, and gives the vortex behavior of transiently growing disturbances.