Surface Properties

Regarding surface properties the classical view in boundary-layer theory is that at surface irregularities, mainly distributed and isolated roughness. The question is, how a roughness influences the transition process. Then it is asked on the one hand (topic 1) how small a roughness must be in order not to lead to an adverse effect, e. g., premature transition. On the other hand (topic 2) it is asked how large a roughness must be in order to trigger turbulence. This is an important topic in ground-facility simulation, if the Reynolds number is not large enough that natural transition can happen. These two topics can be seen under the heading of permissible (topic 1) and necessary (topic 2) surface properties, Section 1.4.

In the field of aerothermodynamics topic 2 in the last decades attained a broader scope. Traditionally it is asked how via a vehicle’s surface boundary – layer stability, laminar-turbulent transition and eventually also turbulence can be controlled. Then tripping devices, for instance, are necessary surface properties.

We count to necessary surface properties besides the classical surface irregularities—if used for this purpose—also the thermal radiation emissiv – ity of the surface, which governs the thermal state of the surface, too, Sec­tion 1.4. The resulting thermal surface effects could be targeted in order to control stability and transition of the boundary layer. It is not known to the author, whether this actually has been considered, because traditionally radiation cooling is seen only in view of the alleviation of thermal loads on the vehicle’s structure.[140]

Means to transfer kinetic, acoustic, internal and chemical energy between instability modes, see, e. g., [79], also can be considered as necessary sur­face properties—seen from the point of view of vehicle design and operation. Such means are studied since many years as devices to effectively control the boundary-layer flow, i. e., the macroscopic behavior of the flow. We mention some of these studies at the end of this sub-section. A special topic is tran­sition in the presence of ablation as it is encountered at ablative thermal protection systems of capsules. We refer in this regard only to the recent review paper [80].

Topic 1: Permissible Surface Properties. Surface irregularities are a sub-set of surface properties. In Section 1.3 we have noted the definition of surface properties as one of the tasks of aerothermodynamics. In the context of laminar-turbulent transition “permissible” surface irregularities include surface roughness, waviness, steps, gaps etc., which are also important in view of fully turbulent flow, Section 8.5. These surface properties should be “sub-critical” in order to avoid either premature transition or amplification of turbulent transport, which both can lead to unwanted increments of viscous drag, and can affect significantly the thermal state of the surface of a flight vehicle and hence the thermal loads on the vehicle’s structure.

On CAV’s all permissible, i. e., sub-critical, values of surface irregularities should be well known, because surface tolerances should be as large as possible in order to minimize manufacturing cost. On RV’s the situation is different in so far as a thermal protection system consisting of tiles or shingles is inherently rough [2], which is not a principal problem with respect to laminar – turbulent transition at altitudes above approximately 40 to 60 km. There transition is unlikely to happen. Below these altitudes a proper behavior and also prediction of transition is necessary in particular in order to avoid adverse increments of the thermal state of the surface.

Surface irregularities in general are not of much concern in fluid mechanics and aerodynamics, because flow past hydraulically smooth surfaces usually is at the center of attention. Surface irregularities are a kind of a nuisance which comes with practical applications. Nevertheless, knowledge is avail­able concerning surface roughness effects on laminar-turbulent transition in hypersonic flow [81].

Surface roughness can be characterized by the ratio k/S1, where к is the height of the roughness and ^ the displacement thickness of the boundary layer at the location of the roughness. The height of the roughness at which it becomes active—with given ^—is the critical roughness height kcr, with the Reynolds number at the location of the roughness, Rek, playing a major role. For к < kcr the roughness does not influence transition, and the surface can be considered as hydraulically smooth. This does not necessarily rule out that the roughness influences the instability behavior of the boundary layer, and thus regular transition. For к > kcr the roughness triggers turbulence and we have forced transition. The question then is whether turbulence appears directly at the roughness or at a certain, finite, distance behind it.[141]

Since a boundary layer is thin at the front part of a flight vehicle, and becomes thicker in down-stream direction, a given surface irregularity may be critical at the front of the vehicle, and sub-critical further downstream.

Permissible surface properties in the sense that clear-cut criteria for sub­critical behavior in the real-flight situation are given are scarce. Usually they are included when treating distributed roughness effects on transition, see, e. g., [2, 42] and also the overviews and introductions [11]—[14]. Some system­atic work on the influence of forward and backward facing steps and surface waviness on transition was performed in a FESTIP study [82].

Permissible surface properties for low speed turbulent boundary layers are given for instance in [24]. Data for supersonic and hypersonic turbulent boundary layers are not known. As a rule the height of a surface irregularity must be smaller than the viscous sub-layer thickness in order to have no effect on the wall shear stress and the heat flux in the gas at the wall.

Topic 2: Necessary Surface Properties. The effectiveness of surface ir­regularities to influence or to force transition depends on several flow para­meters, including the Reynolds number and the thermal state of the surface, and on geometrical parameters, like configuration and spacing of the irreg­ularities. Important is the observation that with increasing boundary-layer edge Mach number, the height of a roughness must increase drastically in order to be effective. For Me ^ 5 to 8 the limit of effectiveness seems to be reached, in the sense that it becomes extremely difficult, or even impossible, to force transition by means of surface roughness [11, 14, 24].

This has two practical aspects. The first is that on a hypersonic flight vehicle at large flight speed not only the Reynolds number but also the Mach number at the boundary-layer edge plays a role. We remember in this con­text the different boundary-layer edge flow parameters at RV’s and CAV’s, which operate at vastly different angles of attack, Fig. 1.3 in Section 1.2. At a RV surface roughness thus can be effective to trigger turbulence once the Reynolds number locally is large enough, because the boundary-layer edge Mach numbers are small, i. e., Me ^ 2.5. In fact the laminar-turbulent transition at the windward side of the Space Shuttle Orbiter with its “rough” TPS tile surface is roughness dominated [2].

Of importance is the case of a single surface roughness. A misaligned tile, for instance, can cause attachment-line contamination (see Sub-Section 8.2.4). In any case a turbulent wedge will be present downstream of it, which may be dissipated soon, if locally the Reynolds number is not large enough to sustain this—premature—turbulence. However, in high-enthalpy flow such a turbulent wedge can lead to a severe hot-spot situation.

The other aspect is that of turbulence tripping in ground-simulation facil­ities, if the attainable Reynolds number is too small. Boundary-layer tripping in the lower speed regimes is already a problem.[142] In high Mach-number flows boundary-layer tripping might require roughness heights of the order of the boundary-layer thickness in order to trigger turbulence. In such a situation the character of the whole flow field will be changed (over-tripping). If more­over the Reynolds number is not large enough to sustain turbulent flow, the boundary layer will relaminarize.

For further details and also surface roughness/tripping effectiveness crite­ria, also in view of attachment-line contamination, see, e. g., [11, 14, 57, 84].

New approaches to the problem of flow control in hypersonic boundary layers, as mentioned above, are the use of micro vortex generators, see, e. g., [85], and localized heating with electro-gasdynamic devices, see, e. g., [86]. Both experimental and numerical studies on boundary-layer response to laser­generated disturbances in a M = 6 flow are reported on in [87, 88].

J. D. Schmisseur, [79], lists studies regarding control of boundary-layer in­stability for instance by acoustic-absorptive surfaces, [89], discrete spanwise roughness elements, [90], and so on. Regarding CAV’s and ARV’s the flow control in view of the inlet performance also is becoming a topic of impor­tance [91]. To develop such approaches into devices working in the harsh aerothermodynamic environment and in view of the systems and integration demands of hypersonic flight vehicles is another task.