Inviscid Aerothermodynamic Phenomena

In Sub-Section 4.3.1 we have seen that if the Reynolds number characterizing a flow field is large enough, we can separate the flow field into inviscid and viscous portions. From Fig. 2.3, Section 2.1, we gather that the unit Reynolds numbers in the flight domain of interest are indeed sufficiently large. This does not mean that aerodynamic properties of hypersonic vehicles can be described fully by means of inviscid theory. This is at best possible for the longitudinal motion of re-entry vehicles.

At transonic, supersonic and hypersonic flight we observe the important phenomenon of shock waves. The shock wave is basically a viscous phe­nomenon, but in general can be understood as a flow discontinuity embedded in an flow field. In this chapter we look at shock waves as compressibility phenomena occurring in the inviscid flow fields past hypersonic flight vehi­cles. We treat their basic properties, and also the properties of the isentropic Prandtl-Meyer expansion. Of importance in hypersonic flight-vehicle design is the stand-off distance of the bow-shock surface at blunt vehicle noses. We investigate this phenomenon as well as the effects of entropy-layer swallowing by the vehicle’s boundary layers.

Also of interest for the development of boundary layers is the change of the unit Reynolds number across shock waves. We will see that an increase of the unit Reynolds number only will occur, if the shock wave is sufficiently oblique. Then a boundary layer behind a shock wave close to the body surface will be thinned. This subsequently changes the thermal state of the surface which influences the skin friction, the heat flux in the gas at the wall and the radiation-adiabatic temperature of the radiation-cooled surface.

Basics of Newtonian flow are considered then. Newtonian flow is an inter­esting limiting case, and the related computation method, with appropriate corrections, is an effective and cheap tool to estimate (inviscid) surface pres­sure and velocity fields. Related to Newtonian flow is the hypersonic shadow effect, which can appear in hypersonic flow past flight vehicles, in particular if they fly at large angle of attack. It is characterized by a concentration of the aerodynamic forces with increasing Mach number at the windward side of the vehicle, the “pressure side” of classical aerodynamics. The leeward side, the “suction side”, is in the “hypersonic shadow” of the body, and loses its

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

DOI: 10.1007/978-3-319-14373-6 _6 role as a force-generating surface. We do not discuss this phenomenon, but refer to [1], where several examples are given, also regarding control-surface efficiency.

The chapter closes with the discussion of a principle being very important for the aerodynamic shape definition and the ground-facility simulation of hypersonic flight vehicles, the Mach-number independence principle.

In this chapter we assume throughout flow with perfect gas. That may be a diatomic gas (air) with 7 = 1.4 or a monatomic gas with 7 = 1.666, Section 5.2. If high-temperature real-gas effects are present in the flow, closed rela­tions like those given in this chapter for perfect gas are not available. However, the Lighthill gas with 7 = 1.333 and the Yeff-approach, see, e. g., [2], to a cer­tain degree permit to treat such flows. Discrete numerical methods of fluid mechanics, however, fully permit to simulate flows with high-temperature real-gas effects, see the examples in Chapter 5.