William S. Saric

Nonparallel stability of boundary‐layer flows

The spatial stability of two‐dimensional incompressible boundary‐layer flows is analyzed using the method of multiple scales. The analysis takes into account the streamwise variations of the mean flow, the disturbance amplitude, and the wavenumber. The theory is applied to the Blasius and the Falkner–Skan flows. For the Blasius flow, the nonparallel analytical results are in good agreement with the experimental data. The results show that the nonparallel effects increase as the pressure gradient decreases.

Stability of Goertler vortices in boundary layers

A formal analysis of Goertler-type instability is presented. The boundary-layer and disturbance equations are formulated in a general, orthogonal, curvilinear system of coordinates constructed from the inviscid flow over a curved surface. Effects of curvature on the boundary-layer flow are analyzed. The basic approximation for the disturbance equations is presented and solved numerically. Previous analyses are discussed and compared with our analysis. It is shown that the general system of coordinates developed in this analysis and the correct order-of-magnitude analysis of the disturbance velocities with two velocity scales leads to a rational foundation for future work in Goertler vortices.

Secondary instability of crossflow vortices

Crossflow-dominated swept-wing boundary layers are known to undergo a highly nonlinear transition process. In low-disturbance environments, the primary instability of these flows consists mainly of stationary streamwise vortices that modify the mean velocity field and hence the stability characteristics of the boundary layer. The result is amplitude saturation of the dominant stationary mode and strong spanwise modulation of the unsteady modes. Breakdown is not caused by the primary instability but instead by a high-frequency secondary instability of the shear layers of the distorted mean flow. The secondary instability has been observed in several previous experiments and several computational models for its behaviour exist. None of the experiments has been sufficiently detailed to allow either model validation or transition correlation. The present experiment conducted using a 45 ◦ swept wing in the low-disturbance Arizona State University Unsteady Wind Tunnel addresses the secondary instability in a detailed fashion under a variety of conditions. The results reveal that this instability is active in the breakdown of all cases investigated, and furthermore, it appears to be well-described by the computational models.

Effect of micron-sized roughness on transition in swept-wing flows

Boundary-layer transition-to-turbulence studies are conducted in the Arizona State University Unsteady Wind Tunnel on a 45-degree swept airfoil. The pressure gradient is designed so that the initial stability characteristics are purely crossflow-dominated. Flow visualization and hot-wire measurements show that the development of the crossflow vortices is influenced by roughness near the attachment-line. Comparisons of transition location are made between a painted surface, a machine-polished surface, and a hand-polished surface. Then, isolated 6 micron roughness elements are placed near the attachment line on the airfoil surface under conditions of the final polish (0.25 micron rms). These elements amplify a centered stationary crossflow vortex and its neighbors, resulting in localized early transition. The diameter, height, and location of these roughness elements are varied in a systematic manner. Spanwise hot-wire measurements are taken behind the roughness element to document the enhanced vortices. These scans are made at several different chord locations to examine vortex growth.

Supersonic laminar flow control on swept wings using distributed roughness

The present work addresses a new technology development that can lead to drag reduction on supersonic aircraft by means of passive laminar flow control (LFC). Recent developments in the understanding of stability and transition in swept-wing flows in low-disturbance environments have offered the promise of controlling transition without the use of complicated systems. The principal control problem with highly swept wings concerns the crossflow instability. It has been demonstrated in a series of low-speed experiments that distributed roughness near the attachment line can control the crossflow instability and can laminarize a boundary layer, provided an induced roughness wavelength is below a critical value. The present work extends this idea to supersonic flow over highly swept wings. The combined computational and experimental work gives design criteria and demonstrates LFC on airfoils swept beyond the characteristic Mach angle i.e. subsonic leading edges.

Passive control of transition in three-dimensional boundary layers, with emphasis on discrete roughness elements

A brief review of laminar flow control techniques is given and a strategy for achieving laminarization for transonic transport aircraft is discussed. A review of some flight-test results on swept-wing transition is presented. It is also shown that polished leading edges can create large regions of laminar flow because the flight environment is relatively turbulence free and the surface finish reduces the initial amplitude of the stationary crossflow vortex.

Effect of leading-edge geometry on boundary-layer receptivity to freestream sound

The receptivity to freestream sound of the laminar boundary layer over a semi-infinite flat plate with an elliptic leading edge is simulated numerically. The incompressible flow past the flat plate is computed by solving the full Navier-Stokes equations in general curvilinear coordinates. A finite-difference method which is second-order accurate in space and time is used. Spatial and temporal developments of the the Tollmien-Schlichting wave in the boundary layer, due to small-amplitude time-harmonic oscillations of the freestream velocity that closely simulate a sound wave travelling parallel to the plate, are observed. The effect of leading-edge curvature is studied by varying the aspect ratio of the ellipse. Boundary layer over the flat plate with a sharper leading edge is found to be less receptive. The relative contribution of the discontinuity in curvature at the ellipse-flat-plate juncture to receptivity is investigated by smoothing the juncture with a polynomial. Continuous curvature leads to less receptivity. A new geometry of the leading edge, a modified super-ellipse, which provides continuous curvature at the juncture with the flat plate, is used to study the effect of continuous curvature and inherent pressure gradient on receptivity.

Non-linear Kelvin–Helmholtz instability

A non-linear analysis is presented for the stability of a liquid film adjacent to a compressible gas and under the influence of a body force directed either outward from or toward the liquid. The effects of the liquids surface tension are taken into account. The non-linear Rayleigh-Taylor instability is included as a special case. The analysis considers the case of an inviscid liquid adjacent to a subsonic flow and the case of a very viscous liquid adjacent to a subsonic or a supersonic flow. For a subsonic external flow, it is found that the cut-off wave-number is amplitude dependent in the inviscid case whereas it is amplitude independent in the viscous case. It is found that the non-linear motion of the gas may be stabilizing or destabilizing, whereas the non-linear motion of the liquid is found to be stabilizing in the viscous case. For a supersonic external flow and a viscous liquid, the cut-off wave-number is amplitude dependent. Moreover, unstable disturbances with wave-numbers near the cut-off wave-number do not grow indefinitely with time but achieve a steady-state amplitude.

Influence of High-Amplitude Noise on Boundary-Layer Transition to Turbulence

Abstract : This work completes a series of detailed experiments of boundary layers undergoing transition to turbulence with the major effort directed toward the most important issue facing the understanding of fundamental causes of transition, i.e., the receptivity to freestream disturbances. This problem is reviewed in detail by Saric et al. (1994). The present effort concentrates on leading-edge receptivity and receptivity of two-dimensional roughness. The effects of large-amplitude freestream noise is considered with the effort directed toward determining the limits of linear receptivity. Single-frequency and broad-band sound waves are used along with 2-D roughness elements to determine how the unstable waves are initiated. New data are presented on leading edge-receptivity that clarify some difficulties with previous experimental work. Comparisons with recent DNS are excellent. Data are also presented for nonlinear receptivity of 2-D roughness elements. It is shown that there is little difference between the single-frequency excitation and white noise in that the response is still keenly triggered by the amplitude of the individual mode. Thus a single frequency at 120 dB is more dangerous than white noise at 120 dB where the energy is distributed of many modes.

Compressible Boundary Layers over Wavy Walls

An analysis is presented of compressible viscous flows past wavy walls without restricting the mean flow to be linear in the disturbance layer. Linearization of the compressible disturbance equations results in a system of six first‐order differential equations for the perturbation quantities. The method of orthonormalization is used to control the error growth in the numerical solution of these equations. The present results agree more closely with experimental data than the results obtained by using Lighthill’s theory, which restricts the mean flow to be linear in the disturbance layer.