Free-Stream Disturbances: The Environment

Under environment we understand either the atmospheric flight environment of a hypersonic flight vehicle or the environment which the sub-scale model of the flight vehicle has in a ground-simulation facility. The question is how the respective environment influences instability and transition phenomena on the flight vehicle or on its sub-scale model [15, 92]. Ideally there should be no differences between the flight environment and the ground-facility en­vironment, but the fact that we have to distinguish between these two envi-

ronments already points to the fact that these environments have different characteristics and different influences on transition. These different influ­ences pose large problems both in view of scientific topics and practical, i. e., vehicle design issues.

The atmosphere, through which a hypersonic vehicle flies, constitutes a disturbance environment. Information about the environment appears to be available for the troposphere, but not so much for the stratosphere, Fig. 2.1. Morkovin suggests, [12], see also [13], as a work hypothesis, that distribution, intensities and scales of disturbances can be assumed to be similar in the troposphere and the stratosphere. Flight measurements in the upper tropo­sphere (11 km altitude) have shown strong anisotropic air motions with very low dissipation and weak vertical velocity fluctuations [93]. How much the flight speed of the vehicle plays a role is not known. This partly will be a matter of the receptivity properties of the boundary layer.

Much is known of the disturbance environment in ground-simulation facil­ities, see, e. g., [11]—[14]. We have mentioned already as major problem noise, i. e., the sound field radiated from the turbulent boundary layers of the tun­nel wall.[143] The quest to create in ground-simulation facilities a disturbance environment similar to that of free flight (whatever that is, see in this regard also [94]) has led to the concept of the “quiet” tunnel, see, e. g., [13].

A Mach 3.5 pilot quiet tunnel has been built in the 1970s in the US at NASA Langley [95]. It is characterized by measures to remove the tur­bulent boundary layer coming from the settling chamber, a new boundary layer developing on the nozzle wall, and finally a sound shield (effectiveness?) enclosing the test section.

The Ludwieg-Tube facilities at the DLR in Gottingen, and at the Tech­nical University Braunschweig, Germany, see, e. g., [96], as well as the Weise – Tube facility of similar principle at the University Stuttgart [97], can not be considered as quiet tunnels. At least the unit Reynolds number effect,[144] see, e. g., [12, 13, 92], has been shown by P. Krogmann not to exist in the Ludwieg tube [98].

The facility at Purdue University is explicitly called a “Mach-6 quiet-flow Ludwieg tube” [99].[145] A recent review of S. P. Schneider sheds light on the capabilities of quiet tunnels today [101]. He mentions, however, that these are only moderate Reynolds number and cold flow tunnels.

The disturbance environment of a flight vehicle or of its sub-scale wind tunnel model is very important, because it provides for regular laminar – turbulent transition:

1. The “initial” conditions in flight and in the ground-simulation facility.

2. The “boundary” conditions in flight (surface conditions, engine noise) and in the ground-simulation facility (tunnel-wall noise, model surface conditions).

Подпись: Tu Подпись: u'2 + v'2 + iv'2 3u4 Подпись: (8.30)

In the aerodynamic practice velocity fluctuations u’, v’, w’, which are also called free-stream turbulence, are the entities of interest. The classical measure is the “level of free-stream turbulence”:

If ■u’2 = v’2 = iv’2, this is called isotropic free-stream turbulence. At low speed, the level of free-stream disturbances strongly governs the transition process. The free-stream turbulence of wind tunnels even for industrial mea­surements should be smaller than Tu = 0.05-0.07 per cent, see, e. g., [102].

A rational and rigorous approach to identify types of disturbances is the consideration of the characteristic values of the system of equations of com­pressible stability theory, see, e. g., [25]. There the following types of distur­bances are distinguished:

— Temperature fluctuations, T’, also called entropy fluctuations.

— Vorticity fluctuations, ш’х, ш’у, u’z.

— Pressure fluctuations, p’, or acoustic disturbances (noise). These are of large importance in hypersonic wind tunnels for M ^ 3, but also in transonic wind tunnels with slotted or perforated walls. Here the limit p’rms/qо = 0.3 per cent is suggested, where q0 is the dynamic pressure of the free-stream [102].

It is interesting to note that for instance at hypersonic flight a free-stream temperature fluctuation can trigger vorticity and acoustic modes while pass­ing the bow-shock surface ahead of the swept leading edge of the wing of the flight vehicle [47].

The environment (free-stream) disturbance properties are of large im­portance especially for non-local non-linear instability methods, which are the basis of non-empirical transition prediction methods, see the following Section 8.4. These methods need a receptivity model. Actually all types of disturbance-transport equations (non-linear/non-local theories) need initial values in the form of free-stream disturbances. These are also needed for the direct numerical simulation (DNS) of stability and transition problems.

The topic of boundary-layer receptivity to free-stream disturbances is discussed in [103]. A comprehensive discussion of the problems of receptivity
models, also in view of the influence of flight speed and flow-field deformation in the vicinity of the airframe as well as the thermal state of the airframe’s surface is still missing.

We note in this context that for the computational simulation of turbulent flows by means of transport-equation turbulence models, for instance of к — є or к — ш type, initial values of the turbulent energy к, the dissipation є or the dissipation per unit turbulent energy ш as free-stream values are needed, too, see, e. g., [10]. A typical value used in many computational methods for the turbulent energy is кж « (0.005 иж)2, whereas ш or є should be “sufficiently small” [104, 105]. Large eddy simulation (LES) of turbulent flow also needs free-stream initial values. The question is whether in non-empirical transition prediction methods for the free-flight situation, apart from surface vibrations and engine noise (relevance of both?), this kind of “white noise” approach is a viable approach. For the ground-facility situation of course the environment, which the facility and the model pose, must be determined and incorporated in a prediction method [101].

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