Laminar-Turbulent Transition as Hypersonic Flow Phenomenon

Laminar-turbulent transition in high-speed flow is a phenomenon with a mul­titude of possible instability and receptivity mechanisms, which depend on a multitude of flow, surface and environment parameters. In the frame of this book only an overview over the most important issues can be given. Detailed introductions to the topic are found in, e. g., [11]—[14].

Possibly two basic transition scenarios can be distinguished, which, how­ever, may overlap to a certain degree:[119]

1. regular transition,

2. forced or by-pass transition.

These two scenarios can be characterized as follows:

— Regular transition occurs if—once a boundary layer is unstable—low – intensity level disturbances, which fit the receptivity properties of the un­stable boundary layer, undergo first linear, then non-linear amplification(s), until turbulent spots appear and actual transition to self-sustained turbu­lence happens. In [15] this is called “transition emanating from exponential instabilities”.

This scenario has been discussed in detail in the classical paper by M. V. Morkovin, [12], see also [13], who considers the (two-dimensional) laminar boundary layer as “linear and non-linear operator” which acts on small disturbances like free-stream vorticity, sound, entropy spots, but also high – frequency vibrations. This begins with linear amplification of Tollmien – Schlichting type disturbance waves, which can be modified by boundary – layer and surface properties like those which occur on real flight-vehicle configurations: pressure gradients, thermal state of the surface, three – dimensionality, small roughness, waviness and so on. It follow non-linear and three-dimensional effects, secondary instability and scale changes and finally turbulent spots and transition.

Probably this is the major transition scenario which can be expected to exist on CAV’s. An open question is how propulsion-system noise and airframe vibrations fit into this scenario.

— Forced transition is present, if large amplitude disturbances, caused, e. g., by surface irregularities, lead to turbulence without the boundary layer acting as convective exponential amplifier, like in the first scenario. Morkovin calls this “high-intensity bypass” transition.

Probably this is the major scenario on RV’s with a thermal protection system (TPS) consisting of tiles or shingles which pose a surface of large roughness. Forced transition can also happen at the junction, of, for in­stance, a ceramic nose cone and the regular TPS, if under thermal and mechanical loads a surface step of sufficient height appears. Similar sur­face disturbances, of course, also can be present on CAV’s, but must be avoided if possible. Attachment-line contamination, Sub-Section 8.2.4, also falls under this scenario.

Boundary-layer tripping on wind-tunnel models, if the Reynolds number is too small for regular transition to occur, is forced transition on purpose. However, forced transition can also be an—unwanted—issue in ground- simulation facilities, if a large disturbance level is present in the test section. Indeed Tollmien-Schlichting instability originally could only be studied and verified in (a low-speed) experiment after such a wind-tunnel disturbance level was discovered and systematically reduced in the classical work of G. B. Schubauer and H. K. Skramstadt [16]. In supersonic/hypersonic wind tunnels the sound field radiated from the turbulent boundary layers of the tunnel walls was shown by J. M. Kendall, [17], to govern transition at M = 4.5, see the discussion of L. M. Mack in [18].

In the following sub-sections we sketch basic issues of stability and tran­sition, and kind and influence of the major involved phenomena. We put emphasis on regular transition.