Laminar-Turbulent Transition and Turbulence in High-Speed Viscous Flow

The state of the boundary layer, laminar or turbulent, strongly influences the thermal state of the surface, in particular if the surface is radiation cooled. The thermal state governs thermal surface effects and thermal loads, as well as the skin friction. Regarding the thermal state, a strong back-coupling exists to the state of the boundary layer. In particular the behavior of hydrodynamic stability, and hence laminar-turbulent transition, are affected by the thermal state of the surface, too.

We have seen that laminar-turbulent transition strongly rises the radia­tion-adiabatic temperature, Figs. 3.3 and 7.10. This is important on the one hand for the structure and materials layout of a hypersonic flight vehicle. On the other hand, transition rises also the wall shear stress, Fig. 7.11, to a large extent. Both the temperature and the shear stress rise are due to the fact that the characteristic boundary-layer thickness of the ensuing turbulent boundary layer, the thickness of the viscous sub-layer, Svs, is much smaller than the characteristic thickness of the—without transition—laminar boundary layer, Fig. 7.6. The latter is the (flow) boundary-layer thickness S.

Boundary-layer turbulence and its modeling is a wide-spread topic also in aerothermodynamics, but perhaps not so much—at least presently—the origin of turbulence, i. e., the phenomenon of laminar-turbulent transition and its modeling.

RV’s in general are not very sensitive to laminar-turbulent transition. Transition there concerns mainly thermal loads. Above approximately 60 to 40 km altitude the attached viscous flow is laminar, below that altitude it becomes turbulent, beginning usually at the rear part of the vehicle. Because the largest thermal loads occur at approximately 70 km altitude [1], the tra­jectory part with laminar flow is the governing one regarding thermal loads. Of course other trajectory patterns than the present baseline pattern, espe­cially also contingency abort trajectories, can change the picture. Transition phenomena, however, may also appear at high altitudes locally on RV’s, for instance, on deflected trim or control surfaces, due to shock/boundary-layer interaction and local separation.

(C Springer International Publishing Switzerland 2015 E. H. Hirschel, Basics of Aerothermodynamics,

DOI: 10.1007/978-3-319-14373-6 _8

Important is the observation that due to the large angles of attack, at least down to approximately 40 km altitude, Fig. 1.3 in Section 1.2, the boundary – layer edge Mach numbers are rather small at the windward side of RV’s.[116] At the windward side of the Space Shuttle Orbiter, the transition location lies at approximately 90 per cent vehicle length at approximately 50 km altitude while a « 35°, and has moved forward to approximately 10 per cent vehicle length at approximately 40 km altitude while a « 30° [2]. This means that on RV’s in general laminar-turbulent transition happens at the windward side actually not in a hypersonic boundary layer, but in an at most low supersonic boundary layer, however one with special properties, Section 1.2.

On (airbreathing) CAV’s, laminar-turbulent transition is not only a mat­ter of thermal loads, but also, since such vehicles are drag-sensitive in general, a matter of viscous drag and of airframe/propulsion integration, see, e. g., [3].

For the US National Aerospace Plane (NASP/X-30) it was reported that the uncertainty of the location of laminar-turbulent transition affects the take-off mass of the vehicle by a factor of two or more [4]. NASP/X-30 was an extremely ambitious project [5]. Strongly influenced by laminar-turbulent transition were mainly thermal loads, viscous drag, and the engine inlet onset flow (height of the boundary-layer diverter).

In the background of such a case looms a vicious snow-ball effect, see, e. g., [6]. Uncertainties in vehicle mass and total drag prediction lead to design margins, see, e. g., [7], which make, for instance, more engine thrust necessary. As a consequence bigger engines and a larger fuel tank volume are needed, hence a larger engine and tank mass, a larger airframe volume and a larger wetted vehicle surface, consequently a larger total drag, and finally a larger take-off mass ensues.

A flight vehicle is weight-critical, or mass-sensitive, if the take-off mass grows strongly with the ratio ‘empty-vehicle mass’ to ‘take-off mass’, see, e. g., [8]. Large mass-growth factors together with small payload fractions are typical for CAV’s. Such vehicles usually are viscous-effects dominated and especially transition sensitive. Laminar-turbulent transition definitely is the key problem in the design of CAV’s and ARV’s.

At CAV’s transition occurs indeed in hypersonic boundary layers. These vehicles typically fly at angles of attack which are rather small, see Fig. 1.3 for the SANGER space transportation system up to separation of the upper stage at about 35 km altitude. Because of the small angles of attack, the boundary-layer edge Mach numbers will be of the order of magnitude of the flight Mach number. At the windward side, with pre-compression in order to reduce the necessary inlet capturing area, the boundary-layer edge Mach number will be somewhat smaller, but in any case the boundary layer also here is a hypersonic boundary layer.

The problems with laminar-turbulent transition and with turbulence are the insufficient understanding of the involved phenomena on the one hand,

and the deficits of the ground-simulation means on the other hand. This holds for both ground-facility and computational simulation.

However, once hypersonic attached viscous flow can be considered as tur­bulent, i. e., if shape and location of the transition zone have been somehow established, it usually is possible to compute the properties of such flow to a fair degree of accuracy, see, e. g., [9, 10], and also Section 7.2. The situa­tion changes negatively if turbulent strong interaction phenomena and flow separation are present.

In hypersonic ground-simulation facilities basically the low attainable Reynolds numbers, the (in general wrong) disturbance environment, which the tunnel poses for the boundary layer on the model, and the thermal state of the model surface are the problems.[117] Either the Reynolds number (though lower than in flight) is large enough for laminar-turbulent transition to occur in a ground-simulation facility, although in general with wrong shape and location of the transition zone due to the wrong disturbance environment and the wrong thermal state of the surface, or artificial turbulence triggering must be em­ployed (where, again, shape and location of the transition zone somehow must have been guessed). In the latter case, too, the Reynolds number still must be large enough to sustain the artificially created turbulence. If that is the case, turbulent attached flow and strong interaction phenomena and separation can be simulated, however, in general without taking into account the proper ther­mal state of the surface. In general the model surface is cold, which is in con­trast to the actual flight situation, see, e. g., Figs. 3.3 and 7.10.

With laminar-turbulent transition the situation is different to that of tur­bulence. Boundary-layer transition is a problem that has plagued several gen­erations of aerodynamicists. There are very few things about transition that are known with certainty, other than the fact that it happens if the Reynolds number is large enough (K. F. Stetson, 1992 [11]). Certainly we know much more about laminar-turbulent transition today than in 1992, but an empir­ical or semi-empirical transition prediction with the needed accuracy and reliability—if a hypersonic vehicle design is viscous-effects sensitive—or even a non-empirical transition prediction, is not yet possible. Unfortunately, an experimental determination of the transition location is also not possible in ground-simulation facilities (see above).

In the following Sections 8.1 to 8.3 we try to draw a picture of the dif­ferent instability and transition phenomena and their dependencies on flow – field parameters and vehicle surface properties, including the thermal state of the surface.[118] In Section 8.4 stability/transition methods and criteria for hypersonic flight-vehicle design purposes are given with due reservations re­garding their applicability and accuracy.

Turbulence in hypersonic flows and its modeling is treated rather briefly and with emphasis on computational simulation in Section 8.5.

Leave a reply

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>