Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M27: BoundaryLayer Instability II 
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Chair: Jill Klentzman, University of Arizona Room: 31C 
Tuesday, November 20, 2012 8:00AM  8:13AM 
M27.00001: Receptivity of highspeed boundary layers with real gas effects Jill Klentzman, Anatoli Tumin The receptivity of high speed boundary layers in chemical nonequilibrium is investigated. A method is developed for the multimode decomposition of boundary layer flows including real gas effects, and the receptivity problem with small disturbances introduced at the wall is examined. The solution of the linearized NavierStokes equations, within the parallel flow approximation, is expressed in the form of normal modes, and the resulting differential equations for the amplitude functions are discretized using fourthorder finite differences. This discretized system is then in the form of a generalized eigenvalue problem, which yields a straightforward definition of the associated adjoint system. A biorthogonality condition is formulated based on the adjoint eigenvectors. Assuming that a complete system of eigenfunctions of the discrete and continuous spectra exists, the biorthogonality condition allows for the projection of a solution onto the discrete modes, which can be utilized in the analysis of DNS results. [Preview Abstract] 
Tuesday, November 20, 2012 8:13AM  8:26AM 
M27.00002: Statistical inverse analysis of supersonic boundarylayer transition Gennaro Serino, Olaf Marxen, Fabio Pinna, Paul Constantine, Catherine Gorle, Gianluca Iaccarino In environments with low boundarylayer disturbance levels representative of free flight in the atmosphere, the laminarturbulent transition process for vehicles moving at supersonic speeds is typically governed by the convective amplification of highfrequency disturbances. A valid statistical characterization of the disturbance spectrum upstream of the transition location is a prerequisite for an accurate prediction of transition. Statistical inverse analysis offers the possibility to provide such a characterization of relevant disturbance spectra. Using measured streamwise distributions of heattransfer coefficients in the transitional zone, an intermittency factor can be defined. The intermittency factor is fed into an inference algorithm based on the Markov chain Monte Carlo method. This approach is applied to infer two characteristic variables, amplitude and frequency, of the disturbance spectrum upstream of the transition location. It relies on the repeated solution of the forward problem, i.e., the computation of intermittency curve given a certain probability density function of the disturbances. The solution of the forward problem employs linearstability theory in conjunction with a critical threshold amplitude for transition. [Preview Abstract] 
Tuesday, November 20, 2012 8:26AM  8:39AM 
M27.00003: Stability of hypersonic compression cones Helen Reed, Joseph Kuehl, Eduardo Perez, Travis Kocian, Nicholas Oliviero Our activities focus on the identification and understanding of the secondmode instability for representative configurations in hypersonic flight. These include the Langley 9310 flared cone and the Purdue compression cone, both at 0 degrees angle of attack at Mach 6. Through application of nonlinear parabolized stability equations (NPSE) and linear parabolized stability equations (PSE) to both geometries, it is concluded that meanflow distortion tends to amplify frequencies less than the peak frequency and stabilize those greater by modifying the boundarylayer thickness. As initial disturbance amplitude is increased and/or a broad spectrum disturbance is introduced, direct numerical simulations (DNS) or NPSE appear to be the proper choices to model the evolution, and relative evolution, because these computational tools include these nonlinear effects (meanflow distortion). [Preview Abstract] 
Tuesday, November 20, 2012 8:39AM  8:52AM 
M27.00004: Azimuthal hotwire measurements in a transitional boundary layer on a flared cone in a Mach 6 quiet wind tunnel Jerrod Hofferth, William Saric Hotwire measurements of secondmode instability waves and the early stages of nonlinear interaction are conducted on a sharptipped, 5$^{\circ}$halfangle flared cone at zero angle of attack in a lowdisturbance Mach 6 wind tunnel at $Re$ = 10$\times$10$^6$ m$^{1}$. Profiles of mean and fluctuating mass flux are acquired at several axial stations along the cone with a bandwidth of over 300 kHz. Frequencies and relative amplitude growth of secondmode instability waves are characterized and compared with nonlinear parabolized stability (NPSE) computations. Additionally, an azimuthal probetraversing mechanism is used to investigate the character of the nonlinear stages of transition occurring near the base of the cone. Recent Direct Numerical Simulations (DNS) of a sharp cone at Mach 6 have shown that a fundamental resonance (or Klebanofftype) breakdown mechanism can arise in the late stages of transition, wherein a pair of oblique waves nonlinearly interacts with the dominant twodimensional wave to create an azimuthal modulation in the form of $\Lambda$vortex structures and streamwise streaks. The azimuthal measurements will identify periodicity qualitatively consistent with these computations and with ``hot streaks'' observed in temperature sensitive paints at Purdue. [Preview Abstract] 
Tuesday, November 20, 2012 8:52AM  9:05AM 
M27.00005: Surface roughness effects on a blunt hypersonic cone Nicole Sharp, Jerrod Hofferth, Edward White The mechanisms through which distributed surface roughness produces boundarylayer disturbances in hypersonic flow are poorly understood. Previous work by Reshotko (AIAA 20084294) suggests that transient growth, resulting from the superposition of decaying nonorthogonal modes, may be responsible. The present study examines transient growth experimentally using a smooth 5degree halfangle conic frustum paired with blunted nosetips with and without quasirandom distributed roughness. Hotwire anemometry in the lowdisturbance Texas A{\&}M Mach 6 Quiet Tunnel shows a slight growth of fluctuations as well as vertical offset due to surface roughness at a range of unit Reynolds numbers. Spectral measurements indicate that the model is subcritical with respect to second mode growth, and azimuthal measurements are used to examine the high and lowspeed streaks characteristic of transient growth of stationary disturbances. [Preview Abstract] 
Tuesday, November 20, 2012 9:05AM  9:18AM 
M27.00006: Characteristics of a streak disturbance induced by an isolated roughness element Kyle Bade, Ahmed Naguib A detailed description of a streak disturbance introduced in a Blasius boundary layer by an isolated roughness element will be presented. This work is motivated by the desire to understand the dependence of the evolution/instability of streamwiseoriented streaks (which play a key role in bypass transition) on the method by which they are generated. The proper scaling of the streamwise evolution of the streak disturbance energy is examined. This expands upon established Re$_{k}^{2}$ scaling (White, et al., Physics of Fluids, 2005) of streak disturbances induced by spanwiseperiodic roughness element arrays. Examining different roughness heights, k, and employing a method that accounts for the streamwise growth of the streak's wallnormal and spanwise scales, it is found that the streak energy density scales with Re$_{k}^{7/3}$, in the case of an isolated roughness element. The data used in the analysis are acquired using hotwire anemometry throughout a threedimensional domain located downstream of a single cylindrical roughness element. These measurements are complemented by smokewire visualizations, which capture clearly three distinct disturbance states, dependent upon roughness element height; namely, stable streaks, streaks with intermittent turbulent bursts, and turbulent disturbances. Correspondence is established between these states and the streamwise evolution of the streak energy and the crossstream disturbance profiles. [Preview Abstract] 

M27.00007: ABSTRACT WITHDRAWN 
Tuesday, November 20, 2012 9:31AM  9:44AM 
M27.00008: Two dimensional roughness effects on hypersonic boundary layer instability Kahei Danny Fong, Xiaowen Wang, Xiaolin Zhong Numerical simulations of 2D roughness effects on modal growth are conducted for a hypersonic boundary layer. Perturbations correspond to pure mode S {\&} mode F at 100 kHz and a wall normal velocity pulse with a frequency spectrum of 1MHz are considered. The evolution of perturbation at different frequency along the streamwise direction with the effect of surface roughness is studied by FFT. Our results show the importance of the relation between roughness location and the synchronization point, where the synchronization point is the point where mode S and mode F have the same phase velocity and synchronizes with each other. Its location can be obtained from the linear stability theory. The results show that if roughness is placed upstream of the synchronization point, perturbation is amplified. The amplification rate depends strongly on roughness height. On the other hand, if roughness is placed close to or downstream of the synchronization point, perturbation is damped. Similar to amplification, the strength of damping depends strongly on roughness height. A tentative explanation is that roughness alters the mean flow profile (ex: sonic line, inflection point). We believe this can be a candidate to explain the roughnessdelayed transition as some experiments have shown. [Preview Abstract] 
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