Numerical simulations of leading-edge acoustic receptivity are performed for a flat-plate with a modified-super-elliptic (MSE) leading edge. For small freestream amplitude, the effect of angle of incidence of the impinging wave is investigated and found to produce higher receptivity coefficients than in the symmetric case. The slope of receptivity coefficient versus angle of incidence of the impinging wave is found to be less than 1/4 of the theoretically predicted slope. This result is not explained by accounting for the finite nose radius of the 6:1 MSE since the Strouhal number based upon the nose radius for these simulations is very small and therefore theory predicts that the receptivity coefficients should be very nearly the same as those for the zero-nose-radius flat plate. There is a small oscillating tangential-velocity component at the attachment line in the simulations. Downstream of the leading-edge region, linear stability theory is found to accurately reproduce the characteristics of the instability waves. At higher, 1% freestream forcing, an instability wave generated by nonlinear interaction is found at double the frequency of the forcing.
[Dc.02] Computation of Acoustic Receptivity for a Transition Experiment
S.S. Collis (Rice University), C.L. Streett (NASA LaRC)
Numerical simulation is used to study the receptivity phase of laminar-to-turbulent transition for conditions which model an experimental investigation for an airfoil geometry, currently underway at NASA LaRC. While the experiment focuses on the later stages of transition, the simulations reported here provide details of the initiation and early growth of instabilities waves, both of which are difficult to measure experimentally. In particular, the simulations are used to examine acoustic receptivity due to the growth of the boundary layer near the leading-edge and due to localized surface roughness. Numerical solutions are obtained by solving the harmonic, linearized Navier--Stokes equations near the airfoil leading-edge subject to a forcing function which represents the interaction of a freestream acoustic disturbance with either the mean boundary layer, in the case of leading-edge receptivity, or the local distortion of the meanflow due to surface roughness. In both cases, the acoustic signature in the boundary layer is determined by solving the linearized, unsteady, boundary-layer equations. The simulations presented here complement the experimental study, helping to provide a more complete database of transition from receptivity to turbulence.
[Dc.03] Receptivity, linear and nonlinear stability of a laminar wall jet
Anatoli Tumin (Tel-Aviv University, Israel)
Receptivity and stability of a two-dimensional laminar wall jet is considered. The wall jet and the disturbance source considered in DNS by S. Wernz and H. F. Fasel (AIAA Paper 96-0079) are chosen for the analysis. The disturbances are introduced by blowing and suction through a slot in the wall. Disturbances of two frequencies (56 and 28 Hz) are considered.. Because in the wall-jet flow two eigenmodes may be unstable, both of them for each frequency are taken into account. Therefore, the linear receptivity problem is solved for two pairs of eigenmodes, and their development and interaction downstream from the source are analyzed. The analysis allows to explain behavior of the fundamental and subharmonic disturbances observed in the numerical simulation. Spectral features of three-dimensional disturbances and wave trains in the wall jet are also considered. The results are presented in figures (http://www.eng.tau.ac.il/\simtumin/DFD97).
[Dc.04] Theoretical and Experimental Comparisons of the Stability and Receptivity of Swept-Wing Boundary Layers
J.D. Crouch (Boeing), V.R. Gaponenko, A.V. Ivanov, Y.S. Kachanov (I.T.A.M.)
Cross-flow instabilities, generated by a time-periodic spatially-localized surface perturbation, are studied in a Falkner-Skan-Cooke boundary layer. In the experiments, the perturbation is produced by a membrane, which is approximated by a linearized boundary condition in the theory. The disturbances are measured at a sequence of downstream positions and decomposed into normal modes. This provides detailed information about the instability wave angles, wave speeds, growth rates, and profile distributions. This information is then used to project upstream to determine the initial-disturbance characteristics. Using in-situ measurements of the membrane shape, the complex receptivity coefficients are determined. The theory assumes a spanwise-independent quasi-parallel flow with a prescribed chordwise edge velocity. The receptivity analysis is based on a non-homogeneous Orr-Sommerfeld problem. Calculated receptivity coefficients are combined with the measured surface geometry to determine initial amplitudes as a function of the spanwise wavenumber. Comparisons between the theory and experiment show good agreement for both the stability and receptivity characteristics.
[Dc.05] DNS of Boundary-layer Receptivity to Freestream Sound for 3-D Hypersonic Flows over a Parabolic Blunt Wedge
Xiaolin Zhong (Mechanical and Aerospace Engineering Department, University of California, Los Angeles)
The receptivity of hypersonic boundary layers to freestream disturbances is altered considerably by the presence of the bow shocks. This paper studies, by direct numerical simulation (DNS), the receptivity of a hypersonic boundary layer to 2-D and 3-D freestream acoustic disturbances for a Mach 15 flow over a parabolic leading edge. The unsteady flow fields between the bow shock and the boundary layer are numerically simulated to study the generation of instability waves in the boundary layer. It was found that the freestream disturbances generated both boundary-layer first and second modes. For all frequencies studied, the first mode is always generated near the leading edge and is amplified before decaying rapidly. The second mode is the dominant mode after the first mode decay. As frequency decreases, the maximum amplitudes and the region of the first mode increases substantially. The DNS shows the generation instability modes of the fundamental forcing frequency is linear. The receptivity also generates nonlinear superharmonics.
[Dc.06] Secondary Instability and Transition Predition for Swept Wing Boundary Layers
Meelan Choudhari, Fei Li, Mujeeb R. Malik (High Technology Corp., Hampton, VA 23666)
Crossflow instability of a 3-D boundary layer is a common cause for transition in swept wing flows. The boundary-layer flow modified by the presence of finite amplitude crossflow modes is susceptible to high-frequency secondary instabilites, which are believed to harbinger the onset of transition. The role of secondary instability in transition prediction is theoretically examined in light of the recent experimental data by Reibert et al. (AIAA Paper 96-0184, 1996). Exploiting the experimental observation that the underlying 3-D boundary layer is convectively unstable, nonlinear PSE is used to compute a new basic state for the secondary instability analysis based on a 2-D eigenvalue approach. The predicted evolution of stationary crossflow vortices is in close agreement with the experimental data. The suppression of naturally dominant crossflow modes by artificial roughness distribution at a subcritical spacing is confirmed. Frequency range of the secondary instability is consistent with that measured in the experiment. Preliminary results indicate that N-factor correlation based on secondary instability growth rates may yield a more robust criterion for transition onset prediction in comparison with an absolute amplitude criterion that is based on primary instability alone.
[Dc.07] Flow Quality amp; Boundary Layer Transition.
J.H. Watmuff (MCAT Inc.), M. Tobak (NASA Ames Rsch. Ctr.)
The widely held view is that transition to turbulence in the Blasius boundary layer occurs via amplification and eventual nonlinear breakdown of initially small amplitude instabilities i.e. Tollmien-Schlichting (TS) waves. However this scenario is only observed for low amplitude free-stream turbulence (FST) levels, i.e. u/U < 0.1%. Bypass of linear TS instability mechanisms occurs for higher FST levels, yet considerable differences exist between the few experiments carefully designed to assess the effect of FST on transition. The consensus is that FST leads to longitudinal streaks that form near the leading edge in the boundary layer. These streaks appear to be regions of concentrated streamwise vorticity and they are often referred to as Klebanoff modes. The importance of mean flow free-stream nonuniformity (FSN) is not as widely appreciated as FST for characterizing wind tunnel flow quality. Here it is shown that, although the wake generated by a d=50\mum wire located upstream of the contraction (Re_d=6.6, x/d=45,000) is immeasurably small by the time it interacts with the leading edge in the test section, it is responsible for generation of a pair of weak streamwise vortices in the boundary layer downstream. The characteristics of these wake-induced vortices and their effect on TS waves are demonstrated. Small remnant FSN variations are also shown to exist downstream of a turbulence grid. The question arises: Are the adverse effects introduced by the turbulence grid caused by FST or by small remnant FSN variations?
[Dc.08] Experiments on Stability and Transition at Mach 3
Paolo Graziosi, G.L. Brown (Princeton University)
A study of stability and transition at Mach 3 has been undertaken. A supersonic wind tunnel of the blowdown type has been developed and thoroughly calibrated to operate at very low stagnation pressures ( 3.5 psia - 10 psia) with a corresponding range of Reynolds number from Re/m = 2 \times 10^6 to Re/m = 5.5 \times 10^6 . At the lowest stagnation pressure with laminar boundary layers on the tunnel walls, the free-stream turbulence level was found to be about .15 per cent. The mean flow over a flat plate has been mapped in detail with the aid of pitot tubes and static probes and accurate comparisons to numerical simulations made. Spectra, growth rates, wave angles, wave speeds and amplitude distributions of naturally occurring instability waves and the background free-stream forcing have been measured using multiple hot wire configurations.
The results have been compared with numerical calculations from stability theory. Measurements of the developing non-linearities and transition and corresponding measurements for forced instability will also be discussed.
[Dc.09] Direct Numerical Simulation of Late Stages of Transition in a Flat Plate Boundary Layer
M.-R. Choi, H. Choi, S.-H. Kang (Seoul National University)
Late stage transition in a flat plate boundary layer is investigated using the direct numerical simulation technique. Inflow disturbance is generated by blowing and suction on the wall (Rist and Fasel, 1995, JFM), which models the effect of the vibrating ribbon used by Kachanov et al. (1985, in Laminar--Turbulent Transition). The computation domain size used covers 115,000 \le Re_x \le 340,000 with the resolution of 1537\times99\times128 grid points. The mean flow quantities such as the skin friction, shape factor and velocity profile show the characteristics of the transition to turbulence. The roll-up of the high shear layer into a new vortex around the lambda vortex is observed and examined in details. As vortical structures associated with this process evolve downstream, spikes and saw tooth-like jumps in velocity signals appear across the boundary layer. The wavenumber-frequency spectral characteristics of the velocities after the second spike stage is being investigated and will be presented. ^\ast Supported by UARC-SNU Contract No. 42.
[Dc.10] Direct Numerical Simulation of Transition to Turbulence in a Curved Channel Flow with Wall Roughness
Bradley Duncan (), Kirti Ghia (Member)
In this study, the influence of wall roughness on the process of transition from laminar to turbulent flow is examined for the flow in a curved channel with periodic distributed surface roughness. Direct numerical simulation of the incompressible Navier-Stokes equations using a single domain spectral method with general curvilinear coordinates is performed in order to compute the temporal evolution of a flow started from rest, and passing through the various stages of the transition process until a turbulent state is reached. The route to transition is determined by the choice of Reynolds number, roughness amplitude and channel curvature. For the present results, transition is observed through growth and subsequent breakdown of streamwise Dean vortices.